LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 

OF" 


Received 
Accession  No.  (o  f  J"£9       -    Class  No. 


ROBINSON'S 


BEGINNER'S    BOOK 


ARITHMETIC 


INTRODUCTORY    TO 


ROBINSON'S  COMPLETE   ARITHMETIC 


mSON,  BLAKEMAN,  GES&ei*;  &  COMPANY 

PUBLISHERS 
NEW   YORK   AND   CHICAGO 


ROBINSON'S 

T  w o  -  B  o  o  K   COURSE 

IN 

ARITHMETIC. 


BEGINNER'S  BOOK  IN  ARITHMETIC.     PRIMARY. 
COMPLETE  ARITHMETIC.     In  one  volume* 


ARITHMETICAL  PROBLEMS.      ORAL  and  WRITTEN. 

KE  YS  to  COMPLETE  ARITHMETIC  and  PROBLEMS, 
in  separate  volumes •,  for   Teachers. 


Arithmetic,  ORAL  and  WRITTEN,  usually  taught 
in  THREE  books,  is  now  offered,  complete  and 
thorough,  in  ONE  book,  "  THE  COMPLETE  ARITHMETIC" 


*  This  COMPLETE  ARITHMETIC  is  also  published  in  TWO  VOLUMES.     PART  I. 
and  PART  II.  are  each  bound  separately,  in  CLOTH. 


Copyright.  1886,  by  IVISON,  BLAKEMAN,  TAYLOJS&  CO. 


A.  &  F.  &  QUNN, 

—  AGENT   FOR"—  - 

IVISON,  BLAKKMAN  &  CO. 
Office  329  Sansome  Street, 


CONTENTS. 


Chapter  1.    Pages  4  to  72,  inclusive. 

Treating  of  the  development  of  numbers,  with  special 
reference  to  the  work  and  requirements  of  pupils  in  the 
Second  Grade.  ^  v  ""-£." 

Chapter  II.    Pages  73  to  147,  inclusive. 

More  advanced  than  Chapter  I.,  and  arranged  with 
reference  to  Third  Grade  work,  with  tables  of  weight, 
measure,  etc. 

Chapter  III.    Pages  148  to  221,  inclusive. 

Fourth  Grade  work.  Eeviewing  the  preceding  and 
treating  of  Keduction,  Bills  and  Accounts,  Cancellation, 
Interest,  etc.,  etc. 


CHAPTER    I. 


SUGGESTIONS  TO  TEACHERS. 

After  the  method  pursued  in  the  first  three  lessons  the 
teacher  will  please  develop  in  the  minds  of  the  pupils  the 
idea  of  the  numbers  from  11  to  20  inclusive,  by  the  use  of 
various  kinds  of  objects,  or  of  lines  upon  the  black-board. 
These  artificial  helps  should  be  abandoned  at  the  earliest 
practicable  moment,  and  the  pupils  led  to  rely  upon  the 
unaided  power  of  the  mind.  The  natural  and  progressive 
development  suggested  in  the  first  three  lessons,  it  is  believed, 
wih1  reduce  the  use  of  these  helps  to  the  minimum.  Two 
aims  in  teaching  numbers  should  always  be  kept  in  mind. 
1st,  To  learn  accuracy  and  facility  in  the  operations  of  Addi- 
tion, Subtraction,  Multiplication  and  Division;  and  2d,  To 
learn  when  these  operations  are  demanded  in  the  solution  of 
concrete  problems. 

The  teacher  will  not  proceed  to  Lesson  IV  until  the  devel- 
opment of  the  numbers  mentioned  above  is  secured. 

The  teacher  should  require  pupils  to  use  complete  senten- 
ces in  answer  to  questions. 


CHAPTER  ONE. 
^LESSON    I. 


NUMBER  11. 

TEACHEE.    Ten  balls  and  one  ball  are  how  many  balls  ? 

PUPIL.    Ten  balls  and  one  ball  are  eleven  balls. 

T.    Eleven  balls  less  one  ball  are  how  many  balls? 

P.    Eleven  balls  less  one  ball  are  ten  balls. 

T.   Nine  books  and  two  books  are  how  many  books  ? 

P.    Nine  books  and  two  books  are  eleven  books. 

T.   Eleven  books  less  two  books  are  how  many  books  ? 

P.    Eleven  books  less  two  books  are  nine  books. 

T.   What  other  two  numbers  of  things  are  eleven  things? 

P.    Eight  things  and  three  things  are  eleven  things ;  or, 

Seven  things  and  four  things  are  eleven  things.     Etc. 
T.   How  is  the  number  eleven  shown  by  figures  ? 
P.    The  number  eleven  is  shown  by  figures  in  this  way :   11. 

11  feet  less  1  foot  are  how  many  feet? 

10  hours  and  how  many  hours  are  11  hours? 
How  many  days  and  1  day  are  11  days  ? 

11  pints  less  how  many  pints  are  10  pints? 
How  many  quarts  less  1  quart  are  10  quarts? 
11  dollars  less  2  dollars  are  how  many  dollars? 
11  miles  less  3  miles  are  how  many  miles? 

9  gallons  and  2  gallons  are  how  many  gallons  ? 
8  pears  and  how  many  pears  are  11  pears? 
11  cents  less  how  many  cents  are  9  cents? 
11  eggs  less  3  eggs  are  how  many  eggs? 
Etc. 


FIRST  BOOK  IN  ARITHMETIC. 
LESSON  II. 

NUMBER   12. 

TEACHEK.   Eleven  chairs  and  one  chair  are  how  many  chairs  ? 

PUPIL.   Eleven  chairs  and  one  chair  are  twelve  chairs. 

T.    Twelve  chairs  less  one  chair  are  how  many  chairs  ? 

P.    Twelve  chairs  less  one  chair  are  eleven  chairs. 

T.    Ten  keys  and  two  keys  are  how  many  keys  ? 

P.    Ten  keys  and  two  keys  are  twelve  keys. 

T.    Twelve  keys  less  two  keys  are  how  many  keys  ? 

P.    Twelve  keys  less  two  keys  are  ten  keys. 

T.   What  other  two  numbers  of  things  are  twelve  things  ? 

P.    Nine  things  and  three  things  are  twelve  things ;  or 

Eight  things  and  four  things  are  twelve  things.     Etc. 
T.    How  is  the  number  twelve  shown  by  figures  ? 
P.    The  number  twelve  is  shown  by  figures  in  this  way :   12. 

12  birds  less  1  bird  are  how  many  birds  ? 

12  pens  less  how  many  pens  are  11  pens? 

How  many  shells  and  1  shell  are  12  shells  ? 

11  berries  and  how  many  berries  are  12  berries? 
How  many  coats  less  1  coat  are  11  coats? 

12  lessons  less  2  lessons  are  how  many  lessons? 
12  corks  less  3  corks  are  how  many  corks  ? 

9  sheep  and  how  many  sheep  are  12  sheep? 
12  peaches  less  4  peaches  are  how  many  peaches  ? 
8  plums  and  how  many  plums  are  12  plums? 
12  melons  less  how  many  melons  are  9  melons  ? 
How  many  cars  are  2  cars  and  10  cars  ? 
Etc. 


CHAPTER  ONE.  7 

LESSON      III. 
NUMBER    13. 

TEACHER.   Twelve  apples  and  one   apple  are  how  many 
apples  ? 

PUPIL.    Twelve  apples  and  one  apple  are  thirteen  apples. 

T.   Thirteen  apples  less  one  apple  are  how  many  apples  ? 

P.    Thirteen  apples  less  one  apple  are  twelve  apples. 

T.   Ten  cherries  and  three  cherries  are  how  many  cherries  ? 

P.    Ten  cherries  and  three  cherries  are  thirteen  cherries. 

T.    Nine  girls  and  four  girls  are  how  many  girls  ? 

P.    Nine  girls  and  four  girls  are  thirteen  girls. 

T.   Thirteen  hats  less  one  hat  are  how  many  hats  ? 

P.    Thirteen  hats  less  one  hat  are  twelve  hats. 

T.   Thirteen  cents  less  four  cents  are  how  many  cents  ? 

P.    Thirteen  cents  less  four  cents  are  nine  cents. 

T.   What  other  two  numbers  of  things  are  thirteen  things  ? 

P.    Eleven  things  and  two  things  are  thirteen  things;  or, 

Nine  things  and  four  things  are  thirteen  things.     Etc. 
T.   How  is  the  number  thirteen  shown  by  figures  ? 
P.    The  number  thirteen  is  shown  by  figures  in  this  way :  13. 

13  stars  less  1  star  are  how  many  stars  ? 

12  hoes  and  how  many  hoes  are  13  hoes  ? 
How  many  dogs  and  3  dogs  are  13  dogs  ? 
How  many  miles  less  4  miles  are  9  miles  ? 

13  horses  less  5  horses  are  how  many  horses  ? 
13  lines  less  how  many  lines  are  10  lines  ? 

9  days  and  how  many  days  are  13  days  ? 
8  buttons  and  how  many  buttons  are  13  buttons  ? 
Etc. 


FIRST  BOOK  IN  ARITHMETIC. 


LESSON   IV. 

2  more  than  11  equals  what? 
2  less  than  12  equals  what? 
2  more  than  12  equals  what  ? 
2  less  than  18  equals  what? 
2  more  than  14  equals  what? 
2  less  than  15  equals  what? 
What  equals  2  more  than  16  ? 
What  equals  2  less  than  17  ? 
What  equals  2  more  than  18  ? 
What  equals  2  less  than  21  ? 
What  equals  2  more  than  21  ? 
What  equals  2  less  than  24  ? 


LESSON  V. 

18  equals  2  more  than  what  ? 
12  equals  2  less  than  what  ? 
14  equals  2  more  than  what? 

14  equals  2  less  than  what? 

15  equals  2  more  than  what? 

16  equals  2  less  than  what? 
2  more  than  what  equals  17  ? 
2  less  than  what  equals  18  ? 
2  more  than  what  equals  19  ? 
2  less  than  what  equals  21  ? 
2  more  than  what  equals  28  ? 
2  less  than  what  equals  22  ? 


LESSON  VI. 

8  more  than  11  equals  what? 
3  less  than  12  equals  what  ? 
8  more  than  18  equals  what? 
8  less  than  17  equals  what  ? 
8  more  than  19  equals  what  ? 
8  less  than  25  equals  what  ? 
What  equals  3  more  than  23  ? 
What  equals  3  less  than  27  ? 
What  equals  3  more  than  29  ? 
What  equals  3  less  than  31  ? 
What  equals  8  more  than  32  ? 
What  equals  3  less  than  36  ? 


LESSON  VII. 

11  equals  3  less  than  what? 

12  equals  3  more  than  what  ? 
15  equals  3  less  than  what? 
17  equals  3  more  than  what? 
19  equals  3  less  than  what? 
21  equals  3  more  than  what? 
8  less  than  what  equals  22  ? 
3  more  than  what  equals  26  ? 
3  less  than  what  equals  28  ? 
3  more  than  what  equals  29  ? 
3  less  than  what  equals  31  ? 
3  more  than  what  equals  35  ? 


CHAPTER  ONE. 


LESSON  VIII. 

4  more  than  11  equals  what? 
4  less  than  13  equals  what? 
4  more  than  15  equals  what? 
4  less  than  17  equals  what  ? 
4  more  than  19  equals  what? 
4  less  than  22  equals  what  ? 
What  equals  4  more  than  24  ? 
What  equals  4  less  than  26  ? 
What  equals  4  more  than  83  ? 
What  equals  4  less  than  39  ? 
What  equals  4  more  than  43  ? 
What  equals  4  less  than  46  ? 


LESSON  IX. 

12  equals  4  less  than  what  ? 
14  equals  4  more  than  what  ? 
16  equals  4  less  than  what? 
20  equals  4  more  than  what  ? 
25  equals  4  less  than  what? 
28  equals  4  more  than  what  ? 
4  less  than  what  equals  33  ? 
4  more  than  what  equals  35  ? 
4  less  than  what  equals  37  ? 
4  more  than  what  equals  42  ? 
4  less  than  what  equals  45  ? 
4  more  than  what  equals  47  ? 


LESSON  X. 

5  more  than  11  equals  what? 
5  less  than  19  equals  what  ? 
5  more  than  16  equals  what? 
5  less  than  22  equals  what  ? 
5  more  than  24  equals  what  ? 
5  less  than  28  equals  what  ? 
What  equals  5  more  than  33  ? 
What  equals  5  less  than  34  ? 
What  equals  5  more  than  44  ? 
What  equals  5  less  than  47  ? 
What  equals  5  more  than  53  ? 
What  equals  5  less  than  59  ? 


LESSON  XL 

11  equals  5  less  than  what? 
17  equals  5  more  than  what? 
19  equals  5  less  than  what? 
23  equals  5  more  than  what  ? 
26  equals  5  less  than  what  ? 
29  equals  5  more  than  what? 
5  less  than  what  equals  32  ? 
5  more  than  what  equals  38  ? 
5  less  than  what  equals  44  ? 
5  more  than  what  equals  45  ? 
5  less  than  what  equals  53  ? 
5  more  than  what  equals  60  ? 


10 


FIRST  BOOK  IN  ARITHMETIC. 


LESSON   XII. 

T.  What  number  equals  5  and  4  ?    P.  9  equals  5  and 
T.  Since  9  equals  5  and  4  it  is  the  sum  of  5  and  4. 
T.  What  number  equals  3  and  5  ?     P.  8  equals  3  and 
T.  What  is  the  sum  of  3  and  5  ?    P.  8  is  the  sum  of  3 
T.  What  is  the  sum  of  4  and  3  ?     P.  7  is  the  sum  of  4 
What  is  the  sum  of  1,  2  and  3  ?     Of  2,  3  and  4  ? 
What  is  the  sum  of  2,  3  and  5  ?     Of  3,  4  and  5  ? 
What  is  the  sum  of  9  and  2  ?       Of  11  and  3  ? 
What  is  the  sum  of  12  and  2  ?     Of  13  and  8  ? 
What  is  the  sum  of  12  and  4  ?     Of  14  and  8  ? 
What  is  the  sum  of  14  and  4  ?     Of  14  and  5  ? 
What  is  the  sum  of  15  and  4  ?     Of  13  and  5  ? 

4. 

5. 
and  5. 
and  3. 

LESSON   XIII. 

LESSON  XIV. 

SUM. 

SUM. 

2 

3 

2 

3 

4 

2 

10 

11 

10 

11 

10 

5 

2 

2 

3 

3 

2 

4 

3 

3 

4 

4 

5 

11 

4 

3 

5 

2 

5 

3 

12 

13 

14 

3 

4 

15 

3 

4 

2 

5 

3 

5 

4 

3 

5 

14 

13 

3 

5 

4 

6 

2 

6 

3 

13 

5 

4 

16 

4 

17 

4 

5 

2 

6 

3 

'    6 

5 

14 

15 

3 

16 

4 

6 

4 

7 

5 

8 

8 

5 

16 

5 

18 

3 

19 

4 

6 

5 

7 

2 

3 

16 

5 

17 

8 

19 

4 

9 

9 

9 

2 

10 

3 

4 

17 

4 

18 

5 

19 

4 

5 

2 

9 

3 

11 

17 

5 

18 

4 

19 

5 

CHAPTER  ONE. 


11 


17 
4 

LESSON  XV. 

SUM. 

4  17   5   18 
17   5  17   2 

2 
18 

12 
11 

LESSON  XVI. 

SUM. 

12   11   13  14 
12  13  12   12 

15 

13 

18 
3 

3 

18 

18 
4 

4 

18 

18 
5 

5 

18 

-13 
13 

14 
14 

15 
14 

15 
12 

16 
12 

13 
16 

19 
2 

2 
19 

19 
8 

3 
19 

19 
4 

4 
19 

17 

22 

21 

22 

22 
23 

23 

24 

24 
24 

24 
25 

19 
5 

6 
19 

21 
2 

2 
21 

21 
8 

3 
21 

25 
22 

25 
23 

25 
24 

32 
25 

33 
24 

35 
23 

21 
4 

4 
21 

21 
6 

5 
21 

22 
4 

5 
23 

35 
b4 

36 
82 

36 
33 

42 
35 

43 
34 

45 
33 

32 

2 

4 
3 

33 
4 

35 
3 

85 
4 

35 
5 

46 

52 

44 

54 

43 
53 

47 

52 

53 
55 

52 
44 

43 

2 

42 
8 

45 
3 

44 
4 

52 
5 

54 

5 

53 
43 

54 
45 

55 
44 

tf4 
45 

56 
43 

57 
42 

11 
3 

23 

4 

55 

2 

56 
5 

58 
3 

59 
5 

51 
45 

52 
33 

53 
44 

54 
35 

55 
84 

56 
42 

12 


FIRST  BOOK  IN  ARITHMETIC. 


LESSON 

XVII. 

LESSON 

XVIII. 

SUM. 

SUM. 

1 

3 

2 

3 

2 

3 

11 

12 

13 

11 

12 

14 

2 

2 

3 

2 

3 

8 

12 

11 

12 

12 

13 

13 

3 

1 

2 

3 

3 

2 

13 

13 

11 

14 

14 

12 

1 

1 

8 

1 

3 

1' 

12 

11 

14 

13 

11 

14 

2 

8 

2 

3 

2 

4 

12 

11 

13 

11 

13 

12 

4 

4 

2 

5  . 

4 

2 

14 

14 

12 

15 

15 

13 

2 

3 

2 

3 

2 

3 

21 

23 

24 

23 

23 

21 

2 

8 

4 

4 

3 

4 

12 

22 

23 

22 

23 

24 

4 

4 

4 

4 

5 

5 

23 

21 

22 

23 

23 

24 

3 

2 

5 

4 

3 

4 

31 

32 

33 

42 

51 

34 

2 

4 

3 

3 

3 

4 

23 

24 

32 

34 

24 

22 

5 

5 

2 

5 

5 

5 

34 

33 

23 

12 

23 

33 

3 

4 

5 

5 

5 

5 

41 

32 

33 

24 

34 

52 

4 

5 

4 

5 

5 

5 

14 

13 

22 

42 

22 

25 

5 

5 

4 

3 

2 

5 

23 

44 

44 

33 

43 

12 

4 

3 

5 

5 

5 

5 

51 

82 

21 

33 

53 

44 

4 

3 

5 

4 

4 

5 

14 

15 

54 

22 

25 

32 

4 

3 

5 

3 

4 

4 

23 

41 

12 

24 

11 

11 

2 

2 

2 

2 

3 

4 

11 

11 

12 

20 

10 

12 

CHAPTER  ONE. 


13 


LESSON  XIX. 

SUM. 

121  122  223  322  243 
212  212  332  233  344 
312  213  134  432  422 


222  532  453  333  222 
313  255  222  254  404 
424  102  301  402  351 


552  403  304  202  830 
204  253  852  344  245 
143  832  223  452  308 


850  505  844  222  505 
423  250  433  505  202 
105  143  120  241  100 


121  212  813  822  855 
343  434  121  233  522 
504  852  844  404  121 


352  512  424  210  243 
204  354  342  445  342 
342  121  233  323  404 


LESSON  XX. 
SUM. 

212  233  413  521  422 
821  342  242  145  845 
121  224  834  223  121 


213  502  405  350  431 
141  153  352  214  305 
425  234  141  225  421 


304  505  321  432  555 
403  350  134  214  111 
250  143  522  352  132 


450  842  425  512  403 
204  405  153  144  232 
222  251  302  223  144 


355  444  324  341  414 
100  211  251  414  852 
343  322  824  200  112 


323  222  804  421  423 
314  333  353  153  243 
251  432  241  322  222 


14 


FIRST  BOOK  IN  ARITHMETIC. 


LESSON    XXI. 

T.  How  much  greater  is  9  than  5  ?     P.  9  is  4  greater  than  5. 

T.  How  much  less  is  5  than  9  ?     P.  5  is  4  less  than  9. 

T.  Since  9  is  4  greater  than  5  and  5  is  4  less  than  9,  4  is  the 

difference  between  5  and  9. 

T.  How  much  more  is  8  than  5  ?    P.  8  is  3  more  than  5. 
T.  How  much  less  is  5  than  8  ?     P.  5  is  3  less  than  8. 
T.  What  is  3  for  that  reason  ?    P.  3  is  the  difference  between 
5  and  8. 

How  much  greater  is  7  than  3  ?    Ans.  7  is  4  greater  than  3. 

How  much  less  is  3  than  7  ?    Am.  3  is  4  less  than  7. 

"What  is  the  difference  between  3  and  7  ?     Ans.  4  is  the 
difference  between  3  and  7. 

What  is  the  difference  between  3  and  8  ?     Of  4  and  8  ? 

What  is  the  difference  between  4  and  7  ?     Of  4  and  9  ? 

What  is  the  difference  between  4  and  10  ?     Of  5  and  12  ? 


LESSON  XXII. 

DIFFERENCE. 

345454 
223331 


6 
2 


7   7 
4   3 


889 
235 


9    10    11    12    13    14 
423542 


15    16    17    18    19   20 
354344 


LESSON  XXIII. 

DIFFERENCE. 

17    18    19    21    22   23 
435243 


24    25    26    27    28   29 
524354 


31    32    35    36    37   38 
243345 


41    42    43    51    54   53 
354454 


CHAPTER  ONE. 


15 


LESSON  XXIV. 

DIFFERENCE. 

23  24  25  25  26  26 
11   11   12  13   12   14 


27  27  28  28  28  28 
13  15  12  14  13  15 


29  29  29  29  33  33 
13  12  14  15  12  21 


34  34  85  35  86  36 
13  21  22  23  22  23 


86  38  88  38  38  38 
24  15  21  22  24  23 


39  39  38  89  89  80 
14   25  15  22  24  23 


45  45  45  46  46  46 
13  22  21  83  34  85 


LESSON  XXV. 

DIFFERENCE. 

47  47  47  48  48  48 
14  23  82   13  24  85 


54  54  64  55  55  55 
13  22  31  13  24  82 


56  56  56  57  57  57 
15  24  33  23  34  42 


58  58  58  59  59  59 
14  83  44  23  82  45 


64  64  64  65  65  65 
32  41  53  33  43  24 


66  66  66  67  67  67 
34  42  54  34  32  45 


68  68  68  69  69  69 
25  83  44  45  54  53 


16 


FIRST  BOOK  IN  ARITHMETIC. 


LESSON    XXVI. 
DIFFERENCE, 

345  432  546   637   567 
121   201  234  333  202 


764  685  576  468  849 
332  321   133  124  325 


968  887  996  986  859 
324  534  534  532  234 


788  847  758  964  869 
335  342  255   121   524 


986  843  468  (>88  799 
521   521   235  235  345 


736  945  867  678  987 
324  482  522  325  543 


694  789  569  999 
145  352  524  245  543 


LESSON  XXVII. 

DIFFERENCE. 

465  564  673  768  876 
231   232  331   423  534 


647  658  768  796  779 
324  335  453  453  432 


869  897  876  874  859 
425  453  434  432  425 


835  748  767  878  898 
312  325  332  523  532 


876  897  765  698  896 
532  432  342  353  353 


637  984  768  786  789 
423  532  225  522  354 


998  899  889  988  999 
453  354   543  345  345 


CHAPTER  ONE.  17 

LESSON    XXVIII. 

ORAL    PROBLEMS. 

1.  John  spent  2  cents  for  candy,  and  2  cents  for  pens.    How 
much  did  he  spend  ? 

2.  A  farmer  sold  a  calf  for  3  dollars  and  a  pig  for  4  dollars. 
How  much  did  he  receive  for  both  ? 

3.  A  ton  of  coal  cost  $6  and  a  cord  of  wood  $4.     What 
is  the  cost  of  both  ? 

4.  One  boy  has  $5  and  another  $3.     How  many  dollars 
have  both  ? 

5.  A  sheep  was  bought  for  $7  and  sold  for  $3  more.     For 
bow  much  was  it  sold  ? 

6.  7  boxes  of  tea  were  sold  to  one  man  and  4  boxes  to 
another.     How  many  boxes  were  sold  ? 

7.  A  boy  rode  9  miles  and  walked  4  miles.     How  far  did 
he  travel  ? 

8.  A  yard  of  velvet  costs  $6,  and  a  yard  of  cloth  f  5.  What 
is  the  cost  of  both  ? 

9.  Robert  gave  8  nuts  to  his  brother  and  kept  4.     How 
many  had  he  at  first  ? 

10.  Sidney  earned  $9  and  Carl  $4.     How  much  did  both 
earn? 

11.  In  a  certain  class  there  are  9  girls  and  5  boys.     How 
many  pupils  are  there  in  the  class  ? 

12.  A  coat  cost  $11  and  a  hat  $3.  What  is  the  cost  of  both  ? 

13.  $12  was  paid  for  a  saddle  and  $4  for  a  bridle.     How 
much  was  paid  for  both  ? 

14.  If  a  slate  cost  11  cents,  and  a  top  4  cents,  what  is  the 
cost  of  both  ? 

15.  There  are  12  boys  in  one  room  and  5  boys  in  another. 
How  many  boys  are  there  in  both  rooms  ? 

16.  13  birds  sit  on  one  tree  and  3  birds  on  another.     How 
many  birds  sit  on  both  trees  ? 


18  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XXIX. 

1.  A  boy  had  14  cents  and  found  4  cents.    How  many  cents 
did  he  then  have  ? 

2.  $14  was  spent  for  a  shawl  and  $3  for  a  bonnet.     How 
much  was  spent  for  both  ? 

3.  How  many  cows  has  a  farmer  if  he  has  14  black  ones 
and  5  white  ones  ? 

4.  John  shot  15  ducks  and  James  shot  4.     How  many  did 
both  shoot  ? 

5.  George  earned  15  cents  in  the  forenoon  and  5  cents  in 
afternoon.     How  much  did  he  earn  in  the  day  ? 

6.  A  boy  counted  16  cars  in  one  train  and  2  in  another. 
How  many  cars  did  he  count  ? 

7.  A  lady  had  $16  leh  after  spending  $3.     How  much 
had  she  at  first  ? 

8.  Mr.  A.  walked  15  miles  in  the  forenoon  and  3  miles  in 
the  afternoon.     How  far  did  he  walk  ? 

9.  Mary  is  16  years  old  and  Jane  is  4  years  older.     How 
old  is  Jane  ? 

10.  Bought  16  yards  of  silk  for  a  dress  and  3  yards  for  a 
jacket.     How  many  yards  were  bought  ? 

11.  George  caught  16  fish  and  Burt  5  fish.     How  many  fish 
did  both  catch  ? 

12.  Andrew  picked  17  roses  and  Jay  4.     How  many  roses 
did  both  pick  ? 

13.  A  whip  costs  17  cents  and  a  top  4  cents.     What  is  the 
cost  of  both  ? 

14.  A  slate  costs  17  cents  and  a  pencil  5  cents.    What  is  the 
cost  of  both  ? 

15.  If  you  read  18  pages  to-day  and  4  to-morrow,  how  many 
pages  do  you  read  both  days  ? 

16.  If  a  pound  of  cheese  costs  18  cents  and  a  bar  of  soap  5 
cents,  what  is  the  cost  of  both  ? 


CHAPTER  ONE. 


LESSON    XXX. 

1.  Paid  $18  for  a  sleigh  and  $5  for  repairing  it.     What 
was  the  cost  of  the  sleigh  ? 

2.  Earned  $19  in  one  day  and  $4  the  next.     How  much 
was  earned  in  both  days  ? 

3.  Paid  $21  for  corn  and  $3  for  oats.     How  much  was 
paid  for  both  ? 

4.  A  boy  had  24  marbles  and  won  4.     How  many  had  he 
then? 

5.  A  drover  had  25  horses  in  one  pasture  and  5  in  another. 
How  many  horses  had  he  in  both  ?. 

6.  Bought  hams  for  $32  and  cider  for  $4.     How  much  was 
paid  for  both  ? 

7.  A  book  costs  34  cents  and  a  pencil  5  cents.     What  is  the 
cost  of  both  ? 

8.  A  farmer  had  35  sheep  and  bought  4.     How  many  sheep 
had  he  then  ? 

9.  A  man  rode  37  miles  and  walked  5  miles.     How  far  did 
he  travel  ? 

10.  It  is  38  miles  from  A  to  B  and  4  miles  further  to  C. 
How  far  is  it  from  A  to  C  ? 

11.  Sold  39  bushels  of  oats  and  3  more  bushels  of  corn. 
How  many  bushels  of  corn  were  sold  ? 

12.  A  boy  lost  38  cents  and  had  5  cents  left.     How  many 
cents  had  he  at  first  ? 

13.  There  are  39  trees  in  one  lot  and  4  in  another.     How 
many  trees  are  in  both  lots  ? 

14.  Took  39  bushels  of  wheat  to  the  mill  at  one  time  and 
5  at  another  time.     How  many  bushels  were  taken  ? 

15.  Paid  $47  for  a  suit  and  $4  for  a  hat.     How  much  was 
paid  for  both  ? 

16.  James  is  48  years  old,  which  is  5  younger  than  William. 
How  old  is  William  ? 


20  FIRST  BOOK  IN  ARITHMETIC. 

LESSON      XXXI. 
WRITTEN     PROBLEMS. 

1.  There  are  15  cows  in  one  field  and  13  in  another.     How 
many  are  there  in  both  fields  ? 

2.  Paid  14  cents  for  a  pound  of  candles  and  12  cents  for 
coffee.     How  much  was  paid  for  both  ? 

3.  Sold  15  pounds  of  butter  and  had  14  pounds  left.    How 
many  pounds  had  I  at  first  ? 

4.  Eddie  earned  16  cents  and  found  13  cents.     How  many 
cents  had  he  then  ? 

6.  Paid  $15  for  a  coat  and  $13  for  a  cloak.     What  is  the 
cost  of  both  ? 

6.  Sarah  wrote  17  lines  and  Jane  12  lines.     How  many 
lines  did  both  write  ? 

7.  John  is  22  years  old  and  his  father  is  25  years  older. 
How  old  is  the  father  ? 

8.  There  are  26  bushels  of  grain   in  one  bin  and  23  in 
another.     How  much  is  there  in  both  bins  ? 

9.  A  farm  contains  33  acres  of  cleared  land  and  25  of  wood 
land.     How  many  acres  in  the  farm  ? 

10.  From  A  to  B  is  35  miles  and  to  C  is  34  miles  further. 
How  far  is  it  from  A  to  C  ? 

11.  There  are  31  days  in  March  and  30  days  in  April.  How 
many  days  are  there  in  both  ? 

12.  Mr.  B  had  32  head  of  cattle,  and  bought  31  more. 
How  many  did  he  then  have  ? 

13.  A  farmer  raised  32  bushels  of  wheat  on  one  acre  and 
44  on  another.     How  many  bushels  did  he  raise  on  both  ? 

14.  A  man  earned  $35  in  May  and  $32  in  June.     How 
much  did  he  earn  in  both  months  ? 

15.  James  had  35  cents,  which  is  33  cents  less  than  John's 
money.    How  much  has  John  ? 


CHAPTER  ONE.  21 

LESSON    XXXII. 

1.  A  boy's  expenses  were  $36  at  Christmas  and  $33  at  New 
Year.     What  were  his  expenses  for  both  days  ? 

2.  One  steeple  is  63  feet  high,  and  another  35  feet  higher. 
How  high  is  the  second  steeple  ? 

3.  Paid  $74  for  a  horse  and  $23  for  a  saddle.     What  is 
the  cost  of  both  ? 

4.  Bought  a  horse  for  $75  and  sold  it  for  $24  more.     For 
what  was  it  sold  ? 

5.  John  has  $64  in  bank,  which  is   $35  less  than   what 
Kobert  has.     How  much  has  Eobert  ? 

6.  A  man  has  46  acres  in  one  lot  and  52  acres  in  another. 
How  much  has  he  in  both  lots  ? 

7.  James  earns  $54  a  month  and  Bruce  $35.     How  much 
do  both  earn  ? 

8.  Bought  a  knife  for  43  cents  and  a  brush  for  54  cents. 
What  is  the  cost  of  both  ? 

9.  Paid  $53  for  wheat  and  $44  for  corn.     How  much  was 
paid  for  both  ? 

10.  Traveled  37  miles  by  boat  and  42  miles  by  rail.     How 
far  did  I  travel  ? 

11.  There  are  31  days  in  January  and  28  in  February. 
How  many  days  are  there  in  both  months  ? 

12.  47  years  is  42  years  less  than  Mr.  B's  age.     How  old 
is  he? 

13.  Mr.  A  sold  53  acres  of  land  to-day  and  44  yesterday. 
How  many  acres  did  he  sell  both  days  ? 

14.  Bought  a  book  for  52  cents  and  a  knife  for  35  cents. 
What  is  the  cost  of  both  ? 

15.  Mary  gathered  54  chestnuts  and  Jane  33  chestnuts. 
How  many  chestnuts  did  they  both  gather  ? 

16.  A  boy  spent  54  cents  and  had  35  cents  left.     How 
much  had  he  at  first  ? 


22  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XXXIII. 

ORAL  PROBLEMS. 

1.  John  had  4  marbles  and  lost  two  of  them.     How  many 
had  he  left? 

2.  George  having  5  cents  spent  3  cents.     How  many  cents 
had  he  left? 

3.  Jane  picked  6  roses  and  gave  away  three  of  them.    How 
many  had  she  left  ? 

4.  4  dollars  were  taken  from  a  box  containing  7  dollars. 
How  many  dollars  were  left  ? 

<5,  5  eggs  were  taken  from  a  nest  containing  8  eggs.     How 
many  eggs  were  left  ? 

6.  Eose  is  9  years  old  and  Kate  is  4  years  younger.     How 
old  is  Kate  ? 

7.  Julia  having  9  peaches  gave  away  3  of  them.     How 
many  were  left  ? 

8.  Ella  bought  9  oranges  and  ate  4  of  them.     How  many 
were  left  ? 

9.  Paid  10  cents  for  a  block  and  3  cents  less  for  paper. 
What  is  the  cost  of  the  paper  ? 

10.  Harry  walked  10  miles  and  Fred  4  miles  less.     How 
far  did  Fred  walk  ? 

11.  May  had  10  credits  and  Leo  5  credits  less.    How  many 
credits  had  Leo  ? 

12.  Bob  earned  f  11  and  paid  $2  for  a  hat.     How  much 
had  he  left? 

13.  Eddie  had  12  marbles  and  lost  all  but  3  of  them.    How 
many  did  he  lose  ? 

14.  Mary  is  12  years  old  and  Blanche  4  years  younger.  How 
old  is  Blanche  ? 

15.  A  book  cost  13  cents  and  a  pencil  3  cents.    How  much 
more  did  the  book  cost  than  the  pencil  ? 


CHAPTER  ONE.  23 

LESSON  XXXIV. 

1.  What  is  the  difference  between  the  cost  of  a  saddle  and 
a  bridle  if  the  saddle  cost  $13  and  the  bridle  $4? 

2.  A  man  traveled  13  miles  while  a  boy  traveled  5  miles. 
How  much  farther  did  the  man  travel  than  the  boy  ? 

3.  Mr.  A.  owed  $14  and  paid  $4  of  it.     How  much  of  it 
remained  unpaid  ? 

4.  From  a  cask  of  water  containing  14  gallons  5  gallons 
leaked  out.     How  much  remained  ? 

5.  From  a  piece  of  cloth  containing  16  yards  5  yards  were 
cut.     How  much  remained  ? 

6.  In  a  pile  of  17  oranges  only  4  are  good.     How  many 
are  bad  ? 

7.  James  earned  $18  and  was  paid  all  but  $5.    How  much 
was  paid  him  ? 

8.  How  much  greater  is  the  cost  of  a  shawl  at  $19  than 
the  cost  of  a  bonnet  at  $4? 

9.  A  gentleman  paid  $3  less  than  $25  for  a  suit  of  clothes. 
How  much  was  paid  for  the. suit? 

10.  The  distance  from  A  to  B  is  26  miles,  which  is  4  miles 
more  than  the  distance  from  A  to  G.     What  is  the  distance 
from  A  to  C  ? 

11.  Sold  a  watch  for  $27,  which  is  $5  more  than  it  cost. 
What  is  the  cost  ? 

12.  4  ducks  were  killed  out  of  a  flock  of  28  ducks.     How 
many  were  left  alive  ? 

13.  From  a  piece  of  silk  containing  29  yards,  5  yards  were 
cut.     How  many  yards  remained  ? 

14.  Out  of  a  lot  of  35  flowers  Euth  took  4.     How  many 
were  left? 

15.  5  gallons  leaked  out  of  a  barrel  containing  81  gallons  of 
molasses.     How  many  gallons  remained? 


24  FIRST  BOOK  IN  ARITHMETIC. 

LESSON   XXXV. 

1.  33  gallons  of  water  were  put  into  a  vessel  and  4  gallons 
leaked  out.     How  many  gallons  remained  ? 

2.  Mary  has  36  peaches,  which  is  5  more  than  Julia  has. 
How  many  has  Julia  ? 

3.  Bought  a  watch  for  $37  and  sold  it  at  a  loss  of  $4. 
How  much  was  received  for  it  ? 

4.  Paid  $42  for  a  sleigh  and  $3  less  for  a  harness.     What 
was  paid  for  the  harness  ? 

5.  A  man  is  43  years  old  and  his  wife  is  4  years  younger. 
How  old  is  his  wife  ? 

6.  Paid  44  cents  for  a  whistle,  which  was  5  cents  too  much. 
What  was  the  true  price  ? 

7.  I  have  45  bushels  of  wheat,  which  is  3  bushels  more 
than  my  corn.     How  much  corn  have  I  ? 

8.  Paid  $4  of  a  debt  of  $46.     How  much  is  yet  unpaid? 

9.  After  traveling  5  miles  of  a  journey  of  49  miles,  how 
much  of  the  journey  is  yet  to  be  traveled? 

10.  One  boy  caught  51  fish  and  another  3  fish.    How  many 
more  did  the  first  catch  than  the  second  ? 

11.  William  had  55  cents  and  spent  all  but  4  cents.     How 
much  did  he  spend  ? 

12.  Paid  $56  for  a  wagon,  which  is  $5  more  than  the  cost 
of  my  cart.     What  is  the  cost  of  the  cart  ? 

13.  A  watch  cost  $57  and  a  ring  $4.     How  much  less  did 
the  ring  cost  than  the  watch  ? 

14.  A  gentleman  paid  all  but  $5  of  a  debt  of  $58.     How 
much  was  paid  ? 

15.  A  farmer  had  59  sheep  and  lost  4  of  them.     How 
many  were  left  ? 

16.  Paid  $58  for  a  wagon,  which  is  $5  more  than  I  paid 
for  a  sleigh.     How  much  was  paid  for  the  sleigh  ? 


CHAPTER  ONE.  25 

LESSON    XXXVI. 

WRITTEN    PROBLEMS. 

1.  Mary  had  25  cents  and  gave  away  12  of  them.     Hciv 
many  had  she  left  ? 

2.  There  are  27  cows  in  one  field  and  14  less  in  another. 
How  many  cows  are  in  the  other  field  ? 

3.  If  you  have  36  buttons  and  lose  23  of  them,  how  many 
have  you  left  ? 

4.  John  has  39  cards  which  is  24  more  than  James  has. 
How  many  has  James  ? 

5.  Lucy  is  15  years  old.     In  how  many  years  will  she  he  39 
years  old? 

6.  A  boy  has  23  cents.     How  much  more  should  he  have  so 
that  he  may  have  38  cents  ? 

7.  A  lady  had  $45  and  lost  aU  but  $21.     How  much  did 
she  lose  ? 

8.  George  earned  $47  to-day  and  $25  less  yesterday.     How 
much  did  he  earn  yesterday  ? 

9.  Of  a  case  of  49  books  24  of  them  were  damaged.     How 
many  were  sound  ? 

10.  Of  a  herd  of  48  cows  32  of  them  were  red  and  the  rest 
white.     How  many  were  white  ? 

11.  A  gentleman  having  $57  lost  $34.     How  much  has 
he  left? 

12.  A  earned  $56  in  May,  which  was  $33  more  than  B 
earned.     How  much  did  B  earn? 

13.  A  lady  is  55  years  old,  which  is  31  years  older  than  her 
daughter.     How  old  is  her  daughter? 

14.  Paid  $57  for  a  wagon,  which  is  $24  more  than  it  cost. 
How  much  did  it  cost? 

15.  C  has  $34.     How  much  more  should  he  have  so  that 
he  may  have  $58? 


26  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XXXVII. 

1.  A  tower  is  58  feet  high,  and  another  one  33  feet  high. 
How  much  higher  is  the  first  than  the  second  ? 

2.  Bought  a  sleigh  for  $64  and  a  saddle   for  $31  less. 
What  was  the  cost  of  the  saddle  ? 

3.  Bought  a  wagon  for  $67  and  sold  it  for  $33.     How 
much  was  lost  ? 

4.  Bought  a  watch  for  $42  and  sold  it  for  $68.    How  much 
was  gained  ? 

5.  From  a  tree  75  feet  high  a  piece  32  feet  long  was  broken 
off.     How  much  was  left  ? 

6.  After  traveling  35  miles,  how  much  farther  should  one 
travel  to  make  a  journey  of  78  miles  ? 

7.  A  gentleman  making  a  journey  of  76  miles  travels  41 
miles  the  first  day.     How  much  of  the  journey  is  left? 

8.  Of  a  list  of  79  words  35  were  misspelled.     How  many 
were  spelled  correctly  ? 

9.  A  man  is  84  years  old  which  is  41  years  older  than  his 
son.     How  old  is  his  son  ? 

10.  A.  lady  is  43  years  old.     In  how  many  years  will  she  be 
79  years  old  ? 

11.  A  man  has  $87.     How  many  dollars  may  he  spend  and 
have  $43  left? 

12.  A  farmer  bought  98  acres  of  land,  all  but  53  acres  of 
which  is  wood  land.     How  much  is  wood  land  ? 

13.  D  had  96  sheep  and  sold  all  but  42  of  them.     How 
many  did  he  sell? 

14.  If  you  have  $43,  how  much  more  do  you  need  so  that 
you  may  have  $97? 

Id.  A  farmer  took  99  eggs  to  market,  and  found  that  35  of 
them  were  broken.     How  many  were  left  whole? 
16.  A  man  is  98  years  old.     How  old  was  he  43  years  ago? 


CHAPTER  ONE. 


27 


2 

4 
6 


8 

10 
12 


LESSON  XXXVIII. 

2  equals  how  many  2's  ? 

4  equals  how  many  2's  ? 

6  equals  how  many  2's  ? 

8  equals  how  many  2's  ? 
10  equals  how  many  2's  ? 
12  equals  how  many  2's  ? 
How  many  2's  equal  14  ? 
How  many  2's  equal  16  ? 
How  many  2's  equal  18  ? 
How  many  2's  equal  20  ? 
How  many  2's  equal  22  ? 
How  many  2's  equal  24  ? 


LESSON    XL. 


1  equals  \ 

2  equals  ^ 

3  equals  J 

4  equals  \ 

5  equals  ^ 

6  equals  ^ 
-^  of  what, 
-|  of  what 
-|  of  what 
^  of  what 
\  of  what 

of  what 


of  what  ? 
of  what  ? 
of  what  ? 
of  what  ? 
of  what  ? 
of  what  ? 
equals  7  ? 
equals  8  ? 
equals  9  ? 
equals  10  ? 
equals  11  ? 
equals  12  ? 


14 
16 
18 


20 
22 

24 


LESSON  XXXIX. 
|-  of  2  equals  what  ? 
^  of  4  equals  what  ? 
^  of  6  equals  what  ? 
^  of  8  equals  what  ? 
1  of  10  equals  what? 
1  of  12  equals  what? 
What  equals  \  of  14? 
What  equals  \  of  16  ? 
What  equals  I  of  18? 
What  equals  £  of  20? 
What  equals  \  of  22  ? 
What  equals^  of  24? 


LESSON    XLI. 

1  equals  what  part  of  2  ? 

2  equals  what  part  of  4  ? 

3  equals  what  part  of  6  ? 

4  equals  what  part  of  8  ? 

5  equals  what  part  of  10  ? 

6  equals  what  part  of  12  ? 
What  part  of  14  equals  7? 
What  part  of  16  equals  8? 
What  part  of  18  equals  9  ? 
What  part  of  20  equals  10? 
What  part  of  22  equals  11  ? 
What  part  of  24  equals  12  ? 


28 


FIRST  BOOK  JLV  ARITHMETIC. 


LESSON   XLII. 


11  and  how 
13  and  how 
16  less  how 
18  less  how 

15  and  how 

16  and  how 

17  less  how 
T9  less  how 

18  and  how 
21  less  how 
21  and  how 
24  less  how 


many 
many 
many 
many 
many 
many 
many 
many 
many 
many 
many 
many 


equal  13  ? 
equal  15? 
equal  14? 
equal  16? 
equal  17  ? 
equal  18? 
equal  15? 
equal  17  ? 
equal  20  ? 
equal  19? 
equal  23  ? 
equal  22  ? 


LESSON  XLIII. 

11  is  what  more  than  9  ? 

12  is  what  less  than  14  ? 

14  is  what  more  than  12  ? 

13  is  what  less  than  15  ? 
16  is  what  more  than  14? 

15  is  what  less  than  17  ? 
What  more  than  16  is  18? 
What  less  than  19  is  17  ? 
What  less  than  18  is  16? 
What  less  than  20  is  18? 
What  less  than  21  is  19? 
What  more  than  21  is  23  ? 


LESSON    XLIV. 

5  equals  how  many  2's? 

5  equals  two  2's  and  1. 

7  equals  how  many  2's  ? 

9  equals  how  many  2's  ? 
11  equals  how  many  2's? 
13  equals  how  many  2's  ? 
How  many  2's  equal  15  ? 
How  many  2's  equal  17  ? 
How  many  2's  equal  19  ? 
How  many  2's  equal  21  ? 
How  many  2's  equal  23  ? 
How  many  2's  equal  25  ? 


LESSON    XLV. 

What  is  1  of  $4? 
What  is  ^  of  6  pencils  ? 
What  is  ^  of  8  books  ? 
What  is  \  of  10  knives  ? 
What  is  ^  of  14  gallons? 
What  is  \  of  12  feet? 
^  of  16  cents  is  what? 
^  of  18  inches  is  what? 
\  of  22  hours  is  what  ? 
\  of  24  acres  is  what  ? 
\  of  20  miles  is  what  ? 
of  a  dozen  is  what  ? 


CHAPTER  ONE. 


29 


3                             15                             27 

6                             18                             30 

9                              21                             33 

12                             24                             36 

LESSON    XLVI. 

LESSON    XLVII. 

How  many  3's  equal  3  ? 

|  of  3  equals  what  ? 

How  many  3's  equal  6  ? 

|  of  6  equals  what  ? 

How  many  3's  equal  9  ? 

|  of  9  equals  what  ? 

How  many  3's  equal  12  ? 

|  of  12  equals  what? 

How  many  3's  equal  15  ? 

-J  of  15  equals  what? 

How  many  3's  equal  18  ? 

^  of  18  equals  what? 

21  equals  how  many  3's? 

What  equals  ^  of  21  ? 

24  equals  how  many  3's  ? 

What  equals  -J-  of  24? 

27  equals  how  many  3's  ? 

What  equals  £  of  27  ? 

30  equals  how  many  3's  ? 

What  equals  l  of  30? 

33  equals  how  many  3's  ? 

What  equals  |  of  33  ? 

36  equals  how  many  3's  ? 

What  equals  -J  of  36  ? 

LESSON    XLVIII. 

LESSON    XLIX. 

1  equals  ^  of  what  ? 

1  equals  what  part  of  3  ? 

2  equals  -3  of  what  ? 

2  equals  what  part  of  6  ? 

8  equals  -|  of  what  ? 

3  equals  what  part  of  9  ? 

4  equals  -|  of  what  ? 

4  equals  what  part  of  12  ? 

5  equals  -J-  of  what? 

6  equals  what  part  of  15  ? 

6  equals  |  of  what  ? 

6  equals  what  part  of  18  ? 

^  of  what  equals  7  ? 

What  part  of  21  equals  7  ? 

3  of  what  equals  8  ? 

What  part  of  24  equals  8  ? 

-3-  of  what  equals  9  ? 

What  part  of  27  equals  9  ? 

-|  of  what  equals  10? 

What  part  of  30  equals  10  ? 

3  of  what  equals  11  ? 

What  part  of  33  equals  11  ? 

I  of  what  equals  12  ? 

What  part  of  36  equals  12  ? 

30 


FIRST  BOOK  IN  ARITHMETIC. 


LESSON   L. 

11  and  how  many  equal  14  ? 

12  less  how  many  equal  9  ? 

13  and  how  many  equal  16  ? 

14  less  how  many  equal  11  ? 

15  and  how  many  equal  18? 
15  less  how  many  equal  12  ? 
17  and  how  many  equal  20  ? 
19  less  how  many  equal  16  ? 
22  and  how  many  equal  25  ? 
27  less  how  many  equal  24  ? 
29  and  how  many  equal  32  ? 
35  less  how  many  equal  32  ? 


LESSON   LI. 

14  is  what  more  than  11  ? 

15  is  what  more  than  12? 
13  is  what  less  than  15  ? 

16  is  what  less  than  19  ? 

17  is  what  more  than  14? 

18  is  what  less  than  21  ? 
What  more  than  19  is  22? 
What  less  than  26  is  23  ? 
What  more  than  25  is  28  ? 
What  less  than  34  is  31  ? 
What  more  than  29  is  32  ? 
What  less  than  37  is  34? 


LESSON    LII. 

5  equals  how  many  3's? 

7  equals  how  many  3's  ? 

8  equals  how  many  3's  ? 

10  equals  how  many  3's? 

11  equals  how  many  3's? 
14  equals  how  many  3's  ? 
How  many  3's  equals  17? 
How  many  3's  equals  20? 
How  many  3's  equals  22  ? 
How  many  3's  equals  26  ? 
How  many  3's  equals  29  ? 
How  many  3's  equals  34  ? 


LESSON    LIIL 

3  of  6  corks  is  what? 
^  of  9  marbles  is  what  ? 
|-  of  12  geese  is  what  ? 
|  of  18  rods  is  what  ? 
3  of  15  minutes  is  what? 
3  of  24  yards  is  what  ? 
What  is  |  of  21  years? 
What  is  I  of  27  months  ? 
What  is  1  of  30  pinks  ? 
What  is  I  of  33  roses  ? 
What  is  1  of  36  days  ? 
What  is     of  a  dozen  ? 


CHAPTER  ONE. 


31 


4 

8 
12 
16 

LESSON  LIV. 
How  many  4's  equal  4  ? 
How  many  4's  equal  8  ? 
How  many  4's  equal  12  ? 
How  many  4's  equal  16  ? 
How  many  4's  equal  20  ? 
How  many  4's  equal  24  ? 
28  equals  how  many  4's  ? 
82  equals  how  many  4's  ? 
36  equals  how  many  4's  ? 
40  equals  how  many  4's  ? 
44  equals  how  many  4's  ? 
48  equals  how  many  4's  ? 


20 
24 
28 
32 


LESSON   LVI. 

1  equals  \  of  what  ? 

2  equals  \  of  what  ? 

3  equals  \  of  what  ? 

4  equals  \  of  what  ? 

5  equals  \  of  what  ? 

6  equals  -J-  of  what  ? 
-J  of  what  equals  7  ? 
•J  of  what  equals  8  ? 
-J-  of  what  equals  9  ? 
|  of  what  equals  10  ? 
\  of  what  equals  11  ? 
\  of  what  equals  12  ? 


36 
40 
44 
48 

LESSON   LV. 
\  of  4  equals  what  ? 
\  of  8  equals  what  ? 
\  of  12  equals  what? 
\  of  16  equals  what? 
\  of  20  equals  what? 
\  of  24  equals  what? 
What  equals  \  of  28  ? 
What  equals  \  of  32  ? 
What  equals  \  of  36  ? 
What  equals  |  of  40  ? 
What  equals  ^  of  44  ? 
What  equals^  of  48? 


LESSON    LVII. 

1  equals  what  part  of  4  ? 

2  equals  what  part  of  8  ? 

3  equals  what  part  of  12  ? 

4  equals  what  part  of  16  ? 

5  equals  what  part  of  20  ? 

6  equals  what  part  of  24  ? 
What  part  of  28  equals  7? 
What  part  of  32  equals  8  ? 
What  part  of  36  equals  9  ? 
What  part  of  40  equals  10  ? 
What  part  of  44  equals  11  ? 

.  What  part  of  48  equals  12  ? 


32 


FIRST  BOOK  IN  ARITHMETIC. 


LESSON  LVIII. 

LESSON  LIX. 

11  and  how  many  equal  15  ? 

15  is  what  more  than  11  ? 

13  less  how  many  equal  9  ? 

12  is  what  less  than  16  ? 

12  and  how  many  equal  16  ? 

17  is  what  more  than  13  ? 

15  less  how  many  equal  11  ? 

19  is  what  less  than  23  ? 

14  and  how  many  equal  18  ? 

22  is  what  more  than  18  ? 

16  less  how  many  equal  12  ? 

25  is  what  less  than  29  ? 

23  and  how  many  equal  27  ? 

What  less  than  30  is  26  ? 

29  less  how  many  equal  25  ? 

What  more  than  27  is  31  ? 

31  and  how  many  equal  35  ? 

What  less  than  41  is  37  ? 

33  less  how  many  equal  29  ? 

What  more  than  41  is  45  ? 

32  and  how  many  equal  36  ? 

What  less  than  44  is  40  ? 

37  less  how  many  equal  33  ? 

What  more  than  45  is  49  ? 

LESSON  LX. 

LESSON  LXI. 

5  equals  how  many  4's  ? 

4  of  8  birds  is  what  ? 

11  equals  how  many  4's? 

^  of  12  mice  is  what? 

14  equals  how  many  4's? 

\  of  16  men  is  what  ? 

19  equals  how  many  4's? 

•£•  of  24  dollars  is  what  ? 

21  equals  how  many  4's? 

\  of  20  miles  is  what  ? 

26  equals  how  many  4's  ? 

^  of  28  pins  is  what  ? 

How  many  4's  equal  31  ? 

What  is  |  of  36  inches  ? 

How  many  4's  equal  38? 

What  is  •!•  of  32  cars  ? 

How  many  4's  equal  43  ? 

What  is  I  of  40  cows  ? 

How  many  4's  equal  47  ? 

What  is  JL  of  36  hats  ? 

How  many  4's  equal  46  ? 

What  is  \  of  44  watches  ? 

How  many  4's  equal  50  ? 

What  is  \  of  48  sheep  ? 

CHAPTER  ONE. 


33 


5                             25                             45 

10                             30                             50 

15                             35                             55 

20                            40                             60 

LESSON  LXII. 

LESSON  LXIIL 

5  equals  how  many  5's  ? 

•g-  of  5  equals  what  ? 

10  equals  how  many  5's  ? 

-|-  of  10  equals  what? 

15  equals  how  many  5's  ? 

|-  of  20  equals  what  ? 

20  equals  how  many  5's  ? 

^  of  15  equals  what? 

25  equals  how  many  5's  ? 

|  of  25  equals  what  ? 

30  equals  how  many  5's  ? 

^  of  85  equals  what  ? 

How  many  5's  equal  35  ? 

What  equals  £  of  80? 

How  many  5's  equal  40  ? 

What  equals  £  of  40  ? 

How  many  5's  equal  45  ? 

What  equals  {•  of  50? 

How  many  5's  equal  50  ? 

What  equals  1  of  45? 

How  many  5's  equal  55  ? 

What  equals  |-  of  55  ? 

How  many  5's  equal  60  ? 

What  equals  |  of  60? 

LESSON  LXIV. 

LESSON  LXV. 

1  equals  £  of  what  ? 

1  equals  what  part  of  5  ? 

2  equals  -J-  of  what  ? 

2  equals  what  part  of  10  ? 

3  equals  |  of  what  ? 

3  equals  what  part  of  15  ? 

4  equals  -J-  of  what  ? 

4  equals  what  part  of  20  ? 

5  equals  ^  of  what  ? 

5  equals  what  part  of  25  ? 

6  equals  |-  of  what  ? 

6  equals  what  part  of  80  ? 

I  of  what  equals  7  ? 

What  part  of  85  equals  7  ? 

£  of  what  equals  8  ? 

What  part  of  40  equals  8  ? 

^  of  what  equals  9  ? 

What  part  of  45  equals  9  ? 

-£-  of  what  equals  10  ? 

What  part  of  50  equals  10? 

|  of  what  equals  11? 

What  part  of  55  equals  11  ? 

•J-  of  what  equals  12  ? 

What  part  of  60  equals  12  ? 

34 


FIRST  BOOK  IN  ARITHMETIC. 


LESSON   LXVI. 


11  and  how  many 
14  less  how  many 

13  and  how  many 

16  less  how  many 

14  and  how  many 

17  less  how  many 
19  and  how  many 
28  less  how  many 
81  and  how  many 
37  less  how  many 
46  and  how  many 
58  less  how  many 


equal  16? 
equal  9  ? 
equal  18? 
equal  11? 
equal  19? 
equal  12? 
equal  24  ? 
equal  23  ? 
equal  30  ? 
equal  32  ? 
equal  51  ? 
equal  53  ? 


LESSON   LXVII. 

16  is  what  more  than  11  ? 
13  is  what  less  than  18  ? 

17  is  what  less  than  22  ? 
21  is  what  more  than  16  ? 
28  is  what  less  than  33  ? 
32  is  what  more  than  27  ? 
What  less  than  44  is  39  ? 
What  more  than  38  is  43  ? 
What  less  than  52  is  47  ? 
What  more  than  49  is  54  ? 
What  less  than  61  is  56? 
What  more  than  57  is  62  ? 


LESSON    LXVIII. 

7  equals  how  many  5's  ? 
13  equals  how  many  5's? 
19  equals  how  many  5's  ? 
23  equals  how  many  5's  ? 
26  equals  how  many  5's  ? 
32  equals  how  many  5's  ? 
How  many  5's  equal  38  ? 
How  many  5's  equal  44  ? 
How  many  5's  equal  48  ? 
How  many  5's  equal  53  ? 
How  many  5's  equal  59? 
How  many  5's  equal  63  ? 


LESSON    LXIX. 

£  of  10  apples  is  what? 
£  of  20  hoys  is  what  ? 
|  of  15  oranges  is  what? 
^  of  25  books  is  what? 
-£  of  35  pins  is  what? 
•J-  of  30  sparrows  is  what  ? 
What  is  |  of  40  days  ? 
What  is  |  of  50  stars  ? 
What  is  |  of  45  cups  ? 
What  is  -J  of  55  rings  ? 
What  is  -J-  of  60  nails  ? 
What  is     of  a  score  ? 


CHAPTER  ONE. 


35 


REVIEW  OF  THE  FACTS. 

LESSON  LXX. 

Three  2's  equal  what?    Two  3's?    Four  2's?     Two  4's? 
Three  3's?    Two  5's?    Five  2's?    Two  6's?     Three  4's? 

Four  3's?     Two  7's?     Three  5's?     Five  3's?  Two  8's  ? 

Four  4's?     Two  9's?     Three  6's?     Four  5's?  Five  4's? 

Three  7's  ?    Two  11' s  ?    Two  12's  ?    Three  8's  ?  Four  6's  ? 


How  many  are  5  times  5  ? 

3  times  9? 

4  times  7? 

3  times  10  ?          5  times  6  ? 

4  times  8? 

3  times  11? 

5'times  7?             3  times  12? 

4  times  9? 

4  times  10? 

5  times  8?            4  times  11? 

5  times  9? 

5  times  10? 

5  times  11?          5  times  12? 

LESSON  LXXI. 

2  what  equal  4?  6?  8?  10?   12?   14?   16?   18? 
20?  22?  24? 

i  of  4  is  what?  6?  8?  10?   12?   14?   16?   18? 
20?  22?  24? 

3  what  equal  6?  9?  12?  15?   18?   21?   24?   27? 
30?  33?  36? 

|  of  6  is  what?  9?  12?  15?   18?  21?  24?   27? 
30?  33?  36? 

4  what  equal  8?  12?  16?  20?   24?   28?   82?   36? 
40?  44?  48? 

i  of  8  is  what?  12?  16?  20?  24?   28?  32?   36? 
40?  44?  48? 

5  what  equal  10?  15?  20?  25?   30?   35?   40?   45? 
50?  55?  60? 

I  of  10  is  what?  15?  20?  25?  30?  85?   40?   45? 
50?  55?  60? 


36 


FIRST  BOOK  IN  ARITHMETIC. 


LESSON    LXXII. 

2  dollars  equal  -|-  of  what? 
2  days  equal  -|  of  what? 
2  miles  equal  -J-  of  what? 

2  sheep  equal  |  of  what? 

3  books  equal  \  of  what? 

3  peaches  equal  |  of  what? 
\  of  what  equals  3  balls? 
|  of  what  equals  3  dollars? 
\  of  what  equals  4  spools? 
\  of  what  equals  4  corks? 
J  of  what  equals  4  shells? 
£  of  what  equals  4  birds? 


LESSON   LXXIII. 


5  fans 
5  hats 
5  letters 

5  rings 

6  men 
6  acres 


equal  -J- 
equal  -J 
equal  \ 
equal  ^ 
equal  \ 
equal  1 


j  of  what  equals 
^  of  what  equals 
\  of  what  equals 
\  of  what  equals 
\  of  what  equals 
\  of  what  equals 


of  what? 
of  what? 
of  what? 
of  what? 
of  what? 
of  what? 
6  hours? 

6  buttons? 

7  blocks? 
7  pints? 
7  quarts? 
7  dimes? 


LESSON    LXXIV. 

8  trees  equal  \  of  what? 
8  girls  equal  \  of  what? 
8  mice  equal  -J-  of  what? 

8  ships  equal  -J-  of  what? 

9  feet    equal  \  of  what? 
9  cars  equal  |  of  what? 

\  of  what  equals  9  pens? 
\  of  what  equals  9  grains? 
\  of  what  equals  10  pages? 
3  of  what  equals  10  dollars? 
\  of  what  equals  10  inches? 
£  of  what  equals  10  hours? 


LESSON  LXXV. 

•J-  of  what  equals  11  women? 
\  of  what  equals  11  acres? 
•J-  of  what  equals  11  cases? 
\  of  what  equals  11  spoons? 
Y  of  what  equals  12  days? 
|  of  what  equals  12  nights? 
12  cents     equal  \  of  what? 
12  hours    equal  £  of  what? 
12  inches  equal  §  of  what? 
12  feet        equal  |  of  what? 
12  marbles  equal  |-  of  what? 
12  cents    equal  |  of  what? 


CHAPTER  ONE.  37 

LESSON    LXXVI. 

1.  If  one  apple  cost  3  cents,  what  is  the  cost  of  2  apples? 

2.  If  one  orange  cost  4  cents,  what  is  the  cost  of  2  oranges? 

3.  At  3  cents  each,  what  is  the  cost  of  3  tops? 

4.  At  5  cents  a  yard,  what  is  the  cost  of  2  yards  of  tape? 

5.  At  4  cents  a  pound,  what  is  the  cost  of  3  pounds  of  flour? 

6.  What  is  the  cost  of  4  feet  of  rope  at  3  cents  a  foot? 

7.  What  is  the  cost  of  5  pencils  at  3  cents  each? 

8.  James  has  7  dollars  and  George  has  2  times  as  many. 
How  many  has  George? 

9.  If  a  man  can  walk  4  miles  an  hour,  how  far  can  he  walk 
in  4  hours? 

10.  Mary  is  8  years  old  and  Sarah  is  2  times  as  old.     How 
old  is  Sarah? 

11.  If  there  are  9  panes  of  glass  in  each  window,  how  many 
panes  are  there  in  2  windows? 

12.  If  a  boy  can  earn  $5  each  week,  how  much  can  he  earn 
in  4  weeks? 

13.  What  is  the  cost  of  2  bonnets  at  $11  each? 

14.  Mr.  A  traveled  7  miles  by  stage  and  3  times  as  far  by  car. 
How  far  did  he  travel  by  car  ? 

15.  James  earns  $12  a  month  and  John  2  times  as  much. 
How  much  does  John  earn  ? 

16.  What  is  the  cost  of  3  yards  of  silk  at  $8  a  yard  ? 

17.  At  $6  a  barrel  what  is  the  cost  of  4  barrels  of  flour? 

18.  John  is  6  years  old,  and  his  father  is  5  times  as  old. 
How  old  is  his  father? 

19.  At  $9  a  ton,  what  is  the  cost  of  5  tons  of  coal? 


38  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    LXXIV. 

1.  At  5  cents  a  quart,  what  is  the  cost  of  5  quarts  of 
berries  ? 

2.  A  man  walked  9  miles  and  rode  3  times  as  far.     How 
far  did  he  ride  ? 

3.  What  is  the  cost  of  4  yards  of  tape  at  7  cents  a  yard  ? 

4.  If  a  man  can  earn  $10  each  week,  how  much  can  he  earn 
in  3  weeks  ? 

5.  What  is  the  cost  of  5  oranges  at  6  cents  each  ? 

6.  At  $8  a  ton,  what  is  the  cost  of  4  tons  of  coal  ? 

7.  At  $11  a  cord,  what  is  the  cost  of  3  cords  of  wood? 

8.  A  boy  earns  $7  a  week  and  his  father  earns  5  times  as 
much.     How  much  does  the  father  earn  ? 

9.  What  is  the  cost  of  3  barrels  of  chestnuts  at  $12  a 
barrel  ? 

10.  Daniel  worked  9  days  and  David  4  times  as  many.   How 
many  days  did  David  work? 

11.  At  10  cents  a  box,  what  is  the  cost  of  4  boxes  of  straw- 
berries? 

12.  If  one  ounce  equals  8  drams,  how  many  drams  do  5 
ounces  equal? 

13.  A  boy  had  11  cents  and  his  father  gave  him  4  times  as 
many.     How  much  did  his  father  give  him? 

14.  What  is  the  cost  of  5  tons  of  hay  at  $9  a  ton? 

15.  At  12  cents  a  pound,  what  is  the  cost  of  4  pounds  of 
sugar? 

16.  At  10  cents  an  hour,  how  much  can  a  boy  earn  in  5 
hours? 

17.  What  is  the  cost  of  5  sheep  at  $11  each? 

18.  If  1  foot  equals  12  inches,  how  many  inches  do  5  feet 
equal? 

19.  What  is  the  cost  of  5  chairs  at  $12  each? 


CHAPTER  ONE.  39 

REVIEW    OF    THE    FACTS.      * 

LESSON    LXXV. 

How  many  2's  are  there  in  6?  8's  in  6?  2's  in  8?  4's 
in  8?  3's  in  9?  2's  in  10?  5's  in  10?  2's  in  12?  3's  in 
12?  4's  in  12?  3's  in  15?  5's  in  15? 

How  many  2's  equal  14?  2's  equal  16?  4's  equal  16? 
2's  equal  18?  3's  equal  18?  2's  equal  20?  4's  equal  20? 
5's  equal  20?  2's  equal  22?  21s  equal  24?  3's  equal  24? 
4's  equal  24? 

27  equals  bow  many  3's?  28  how  many  4's?  30  how 
many  3's?  30  how  many  5's?  32  how  many  4's?  33  how 
many  3's?  35  how  many  5's?  36  how  many  3's?  36  how 
many  4's? 

How  many  times  4  is  40?  5  is  40?  4  is  44?  5  is  45? 
4  is  48?  5  is  50?  5  is  55?  5  is  60? 


LESSON  LXXVI. 

I  of  4  is  what?  |  of  4?  \  of  6?  %  of  6?  f  of  6? 
§  of  6?  \  of  8? 

\  of  8  is  what?  f  of  8?  \  of  8?  f-  of  8?  \  of  9? 
|-  of  9? 

\  of  10  is  what?  |  of  10?  f  of  10?  |  of  10?  £  of  10? 
f  of  10? 

\  of  12  is  what?  J  of  12?  f  of  12?  \  of  12?  f  of  12? 
\  of  12? 

i  of  14  is  what?    \  of  15?    -f  of  15?    \  of  15?     \  of  16? 

\  of  16  is  what?    £  of  J6?    \  of  16?    \  of  18? 

|  of  18  is  what?     |  of  18?    \  of  20?     f  of  20?    |  of  20? 

|  of  20  is  what?  f  of  20?  §.  of  20?  £  of  20?  |  of  21  ? 
f  of  21? 

|  of  22  is  what?  |  of  24?  f  of  24?  \  of  24?  f  of  24? 
f  of  24? 


40  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    LXXX. 

What  is  the  J-  of  25?  fof25?  fof25?  fof25?  |  of  27? 
|  of  27?  |  of  28?  |  of  28?  \  of  28? 

What  is  the  £  of  30?  |of30?  |of80?  |of30?  |of30? 
f  of  30? 

What  is  the  £  of  32?    fof32?    fof32?    -i  of  33?    fof33? 

What  is  the  |  of  35?  fof35?  |  of  35?  fof35?  |of36? 
|  of  36? 

What  is  the  i  of  36?  |of36?  fof36?  |of40?  £of40? 
|  of  40? 

What  is  the  |  of  40?  |  of  40?  |  of  40?  f  of  40?  |  of  44? 
-£-  of  44?  |  of  44? 

What  is  the  |  of  45?  f  of  45?  f  of  45?  |  of  45? 
\  of  48?  |  of  48?  f  of  48? 

What  is  the  |  of  50?  |  of  50?  f  of  50?  |  of  50? 
I  of  55?  I  of  55?  |  of  55?  |  of  55? 

What  is  the  £  of  60?      |  of  60?      |  of  60?      |  of  60? 


LESSON    LXXXI. 

|  of  what  is  2?  |  of  what  is  4?  \  of  what  is  6?  \  of 
what  is  8? 

\  of  what  is  9?  \  of  what  is  11?  \  of  what  is  12? 
|  of  what  is  12? 

|  of  what  is  6?  \  of  what  is  7?  \  of  what  is  10?  \  of 
what  is  12? 

|  of  what  is  4?  f  of  what  is  8?  f  of  what  is  12?  |  of 
what  is  12? 

\  of  what  is  5?  \  of  what  is  7?  \  of  what  is  9?  \  of 
what  is  11? 

I  of  what  is  6?  \  of  what  is  9?  f  of  what  is  12?  f  of 
what  is  16? 

\  of  what  is  7?  |  of  what  is  9?  f  of  what  is  12?  |  of 
what  is  16? 


CHAPTER  ONE.  41 


LESSON    LXXIX. 

1  yard  =  3  feet.        1 12  inches  =  1  foot.     1  inch  =  TTT  foot. 


1  foot  =  12  inches.  I    3  feet  =  1  yard. 


1  foot  —  -J-  yard. 


2  yards  equal  how  many  feet?  3  yards?  4  yards? 
5  yards? 

6  feet  equal  how  many  yards?  9  feet?  12  feet?  15  feet? 
18  feet?  24  feet?  27  feet?  86  feet? 

1  of  3  feet  is  what?    -J-  of  1  yard  equals  what?     2  yards? 
3  yards?     4  yards?     6  yards?     9  yards?     12  yards? 

2  feet  equal  how  many  inches?     3  feet?     4  feet?     6  feet? 


LESSON    LXXX. 

1  gallon  =4  quarts.   2  pints  =  1  quart.      1  pint  =  \  quart. 
1  quart  =  2  pints.     4  quarts  =  1  gallon.    1  quart  =  \  gallon. 

2  gallons  equal  how  many  quarts?  8  gallons?  4  gallons? 
5  gallons? 

8  quarts  equal  how  many  gallons?  12  quarts?  16  quarts? 
24  quarts?  32  quarts?  36  quarts?  48  quarts? 

-J  of  4  quarts  is  what?  \  of  1  gallon  equals  what?  2  gal- 
lons? 3  gallons?  5  gallons?  7  gallons?  9  gallons?  12 
gallons? 

2  quarts  equal  how  many  pints?  8  quarts?  4  quarts? 
5  quarts? 

4  pints  equal  how  many  quarts?  6  pints?  8  pints? 
12  pints?  14  pints?  16  pints?  18  pints?  22  pints? 
24  pints? 

^  of  2  pints  is  what?  \  of  1  quart  is  what?  2  quarts? 
3  quarts?  6  quarts?  8  quarts?.  10  quarts?  12  quarts? 


42  FIRST  BOOK  IN  ARITHMETIC. 


LESSON    LXXXI. 


1  year =12  months. 
1  year =52  weeks. 
1  week =7  days. 
1  day =24  hours. 
1  hour =60  minutes. 
1  minute =60  seconds. 


60  seconds =1  minute. 
60  minutes =1  hour. 
24  hours =1  day. 
7  days=l  week. 
52  weeks =1  year. 
12  months =1  year. 


2  years  equal  how  many  months?  3  years?  4  years? 
5  years? 

1  of  12  months  is  how  many  months?     ^  of  a  year  is  how 
many  months? 

J  of  a  year  is  how  many  months?  f  of  a  year?  J  of  a 
year?  -f  of  a  year?  f  of  a  year? 

2  weeks  equal  how  many  days?       8  weeks?      4  weeks? 
5  weeks? 

£  of  24  hours  is  how  many  hours?  %  of  a  day  is  how 
many  hours? 

^  of  a  day  is  how  many  hours?  §  of  a  day?  ^  of  a  day? 
|  of  a  day?  f  of  a  day? 

I  of  60  minutes  is  how  many  minutes?  -f  of  an  hour  is 
how  many  minutes?  f  of  an  hour?  f  of  an  hour?  f  of 
an  hour? 

^  of  60  seconds  is  how  many  seconds?  ^  of  a  minute  is 
how  many  seconds?  f  of  a  minute?  f  of  a  minute?  |  of 
a  minute? 

1  foot  equals  what  part  of  1  yard?     What  part  of  2  yards? 

1  inch  equals  what  part  of  1  foot?  2  inches?  3  inches? 
4  inches? 

1  pint  equals  what  part  of  1  quart?  1  quart  equals  what 
part  of  1  gallon?  2  quarts? 

1  month  equals  what  part  of  1  year?  2  months? 
3  months?  4  months? 


CHAPTER  ONE.  43 

LESSON    LXXXII. 

1.  What  is  the  cost  of  \  of  a  ton  of  coal  if  1  ton  costs  $6? 

2.  How  much  should  be  paid  for  £  of  a  yard  of  velvet  if  1 
yard  costs  $8? 

3.  If  a  quantity  of  flour  costs  $18,  what  is  the  cost  of  \ 
of  the  quantity? 

4.  If  a  man  can  walk  24  miles  one  day,  how  far  can  he 
walk  in  ^  of  a  day? 

5.  What  is  the  cost  of  ^  of  a  cord  of  wood,  if  one  cord 
costs  $12? 

6.  James  has  $18  and  Joe  has  J  as  much.     How  much 
money  has  Joe? 

7.  John's  father  can  earn  $24  a  week,  and  he  can  earn  ^ 
as  much?    How  much  can  John  earn  a  week? 

8.  If  it  costs  86  cents  to  ride  a  certain  distance,  what  is  the 
cost  of  riding  J  as  far? 

9.  What  is  the  value  of  £  of  an  acre  of  land  if  one  acre 
costs  $20? 

10.  If  an  engine  runs  28  miles  in  one  hour,  how  far  does  it 
run  in  J  of  an  hour? 

11.  How  much  board  does  a  man  pay  for  ^  of  a  month  if 
he  pays  $32  for  one  month? 

12.  If  a  man  receives  $48  for  digging  a  trench,  how  much 
does  he  receive  for  ^  of  the  work? 

13.  Mr.  A.  is  30  years  of  age  and  his  son  is  \  as  old.  How 
old- is  the  son? 

14.  Mr.  B.  pays  for  rent  $35  a  month.     How  much  does 
he  pay  for  |  of  a  month? 

15.  James  wrote  45  words,  \  of  which  are  misspelled.  How 
many  were  misspelled? 

16.  During  a  storm  it  rained  one  hour  and  hailed  ^  as  long. 
How  many  minutes  did  it  hail?- 


44 


FIRST  BOOK  IN  ARITHMETIC. 


LESSON    LXXXIII. 


How  many  times 
2  pints  are  4  pints? 

2  pints  are  6  pints? 

3  pints  are  6  pints? 

2  quarts  are  8  quarts? 

4  quarts  are  8  quarts? 

3  gallons  are  9  gallons? 
2  apples  are  10  apples? 

5  apples  are  10  apples? 

2  melons  are  12  melons? 

3  melons  are  12  melons? 

4  melons  are  12  melons? 


How  many  times 
2  balls  are  14  balls? 
8  balls  are  15  balls? 
5  balls  are  15  balls? 
2  dollars  are  16  dollars? 
4  dollars  are  16  dollars? 

2  peaches  are  18  peaches? 

3  peaches  are  18  peaches? 

2  cherries  are  20  cherries? 

4  cherries  are  20  cherries? 

5  cherries  are  20  cherries? 

3  plums  are  21  plums? 


LESSON    LXXXIV. 


How  many  times  are 
2  quinces  in  22  quinces? 

2  pears  in  24  pears? 

3  pears  in  24  pears? 

4  pears  in  24  pears? 

5  feet  in  25  feet? 

3  inches  in  27  inches? 

4  miles  in  28  miles? 

3  years  in  30  years? 

5  years  in  30  years? 

4  days  in  32  days? 

3  hours  in  33  hours? 


How  many  times  are 
5  yards  in  35  yards? 

3  pounds  in  36  pounds? 

4  pounds  in  36  pounds? 

4  acres  in  40  acres? 

5  acres  in  40  acres? 

4  lemons  in  44  lemons? 

5  dates  in  45  dates? 

4  corks  in  48  corks? 

5  cents  in  50  cents? 

5  acorns  in  55  acorns? 
5  boxes  in  60  boxes? 


CHAPTER  ONE.  45 

LESSON    LXXXV. 

1.  At  $6  a  yard,  what  is  the  cost  of  2  yards  of  velvet? 

2.  If  two  yards  of  velvet  cost  $12,  what  is  the  cost  of  one 
yard? 

3.  At  $2  a  yard  how  many  yards  of  cloth  can  be  bought 
for  f  12. 

4.  If  a  boy  can  earn  $8  each  week,  how  much  can  he  earn 
in  3  weeks? 

5.  If  $24  can  be  earned  in  3  weeks,  how  much  can  be  earned 
in  one  week? 

6.  At  $3  a  day,  in  how  many  days  can  a  man  earn  $24? 

7.  If  one  ton  of  coal  cost  $7,  what  is  the  cost  of  4  tons? 

8.  If  4  tons  of  coal  cost  $28,  what  is  the  cost  of  one  ton? 

9.  At  4  miles  an  hour,  in  how  many  hours  can  a  man  walk 
28  miles? 

10.  If  one  sheep  cost  $9,  what  is  the  cost  of  5  sheep? 

11.  If  5  sheep  cost  $45,  what  is  the  cost  of  one  sheep? 

12.  At  5  cents  each,  how  many  pencils  can  be  bought  for 
45  cents? 

13.  How  many  oranges  at  4  cents  each  can  be  bought  for 
24  cents? 

14.  If  3  tops  cost  21  cents,  what  is  the  cost  of  one  top? 
Id.  How  many  ounces  of  drugs  at  $2  an  ounce,  can  be 

bought  for  $14? 

16.  If  4  dozen  of  eggs  cost  28  cents,  what  is  the  cost  of 
one  dozen? 

17.  At  $3  a  yard,  how  many  yards  of  silk  can  be  bought 
for  $27? 

18.  If  5  boys  earn  $35,  how  much  does  each  boy  earn? 

19.  At  $5  a  barrel,  how  many  barrels  of  flour  cost  $30? 


46  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    LXXXVI. 

1.  At  $2  a  pair,  how  many  pairs  of  skates  cost  $24? 

2.  If  2  pounds  equal  24  ounces,  how  many  ounces  does  one 
pound  equal? 

3.  Since  4  quarts  equal  one  gallon,  how  many  gallons  do 
48  quarts  equal? 

4.  At  5  cents  a  yard,  how  many  yards  of  tape  cost  60 
cents? 

5.  If  3  bunches  of  radishes  cost  12  cents,  what  is  the  cost 
of  1  bunch? 

6.  At  $3  a  head,  how  many  head  of  sheep  can  be  bought 
for  $18? 

7.  At  4  cents  each,  how  many  oranges  can  be  bought  for  28 
cents? 

8.  If  4  lemons  cost  32  cents,  what  is  the  cost  of  1  lemon? 

9.  What  is  the  cost  of  1  paper  of  needles  if  5  papers  cost 
35  cents? 

10.  How  many  bunches  of  grapes,  at  5  cents  each,  can  be 
bought  for  40  cents? 

11.  Paid  $24  for  3  head  of  sheep.   What  is  the  cost  of  each 
head? 

12.  If  4  quarts  of  molasses  cost  36  cents,  what  is  the  cost 
of  1  quart? 

13.  If  5  tons  of  hay  cost  $60,  what  is  the  cost  of  1  ton? 

14.  How  many  quarts  of  oil,  at  3  cents  a  quart,  can  be 
bought  for  36  cents? 

15.  Since  4  pecks  equal  1  bushel,  how  many  bushels  do 
44  pecks  equal? 

16.  At  $5  a  day,  in  how  many  days  can  a  man  earn  $60? 


CHAPTER  ONE.  47 

LESSON    LXXXVII. 

1.  If  2  men  can  do  a  piece  of  work  in  4  days,  in  what  time 
can  1  man  do  it? 

2.  'If  1  man  can  make  a  sled  in  15  days,  in  what  time  can 
3  men  make  it? 

3.  In  what  time  can  1  man  dig  a  ditch,  if  4  men  can  dig  it 
in  6  days? 

4.  In  what  time  can  5  men  mow  a  field  of  grass,  if  1  man 
can  do  it  in  40  days? 

5.  If  2  boys  can  earn  a  certain  sum  in  9  days,  in  what  time 
can  1  boy  earn  it? 

6.  In  what  time  can  3  men  build  a  fence,  if  1  man  can 
build  it  in  2  days? 

7.  In  what  time  can  1  man  lay  a  stone  wall,  if  4  men  can 
lay  it  in  9  days? 

8.  If  5  persons  consume  a  barrel  of  cider  in  10  days,  in 
what  time  can  1  man  drink  it? 

9.  If  1  man  can  drink  a  quantity  of  tea  in  36  days,  how 
long  will  it  last  3  men? 

10.  In  what  time  can  1  boy  build  a  dam,  if  4  boys  can  do 
it  in  12  days? 

11.  In  what  time  can  5  men  earn  a  given  sum  of  money,  if 
1  man  can  earn  it  in  60  days? 

12.  If  1  man  can  do  a  piece  of  work  in  4  days,  what  part 
of  it  can  he  do  in  1  day?    In  2  days? 

13.  If  a  ship  sails  a  certain  distance  in  6  days,  what  part 
of  the  distance  does  it  sail  in  1  day?     In  2  days?    In  3  days? 

14.  What  part  of  a  fence  can  a  man  build  in  1  day,  if  he 
can  build  it  all  in  8  days?    What  part  in  2  days?    In  4  days? 

15.  What  part  of  a  barrel  of  flour  does  a  family  consume 
in  1  week,  if  they  consume  it  all  in  10  weeks?     What  part 
in  2  weeks?    In  5  weeks? 


48  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    LXXXVIII. 

TEACHER.  What  number  equals  3  times  4  ?  PUPIL.  12  equals 
3  times  4. 

T.  What  number  equals  4  times  3  ?    P.  12  equals  4  times  3. 

T.  Because  12  equals  3  times  4,  or  4  times  3,  it  is  the  pro- 
duct of  3  and  4. 

T.  What  is  the  product  of  3  and  5?  P.  15  is  the  product 
of  3  and  5. 

What  is  the  product  of  2  and  3?  2  and  4?  8  and  3? 
2  and  5?  2  and  6?  3  and  4?  2  and  7?  3  and  5?  2  and  8? 

What  is  the  product  of  4  and  4?     2  and  9?     3  and  6? 

2  and  10?       4  and  5?       3  and  7?       2  and  11?       2  and  12? 

3  and  8? 

What  is  the  product  of  4  and  6?     5  and  5?     3  and  9? 

4  and  7?       3  and  10?       5  and  6?       4  and  8?       3  and  11? 

5  and  7? 

What  is  the  product  of  3  and  12?  4  and  9?  4  and  10? 
5  and  8?  4  and  11?  5  and  9?  4  and  12?  5  and  11? 
5  and  12? 

LESSON    LXXXIX. 

PENCIL  EXERCISES.    PRODUCTS. 

7J  2  34          3  5  6  4  7 

-*•  "^22232232 

58496         10  5  7 

^•"^32428248 

11         12  8  6  5  9  7          10 

*'  ^  223453  4  3 

6          8         11  7         12  9         10  8 

54853445 

11  9         12         10         11         12 

454555 


CHAPTER  ONE.  49 

LESSON     XC. 

TEACHER.  How  many  2's  are  there  in  6  ?  PUPIL.  Three 
2's  are  in  6. 

T.  How  many  times  is  2  contained  in  6  ?  P.  2  is  con- 
tained 3  times  in  6. 

T.  Because  three  2's  are  in  6,  or  2  is  contained  3  times  in 
6,  3  is  the  quotient  of  6  and  2. 

T.  What  is  the  quotient  of  6  and  3  ?  P.  Two  is  the  quo- 
tient of  6  and  3. 

What  is  the  quotient  of  8  and  2  ?,  8  and  4  ?  9  and  8  ? 
10  and  2 ?  10  and  5  ?  12  and  2?  12  and  3?  12  and  4? 

What  is  the  quotient  of  14  and  2?  15  and  3?  15  and  5  ? 
16  and  4  ?  18  and  2  ?  18  and  3  ?  20  and  2  ?  20  and  4? 

What  is  the  quotient  of  20  and  5  ?  21  and  3  ?  22  and  2  ? 
24  and  2?  24  and  3?  24  and  4?  25  and  5?  27  and  3? 

What  is  the  quotient  of  28  and  4  ?  30  and  3  ?  30  and  5  ? 
82  and  3 ?  33  and  8 ?  35  and  5?  36  and  3?  36  and  4? 

What  is  the  quotient  of  30  and  3  ?  30  and  5  ?  32  and  4  ? 
40  and  4 ?  40  and  5  ?  44  and  4?  45  and  5?  48  and  4? 


LESSON    XCI. 

PENCIL    EXERCISES. 

Quotient. 

2)4_  2)6^  3)6^  2)8_  4)8^  3)9_  2)10^  5)10^ 

2)12_  3)12^  4)12^  2)1£  3)15^  5)15^  2)16  4)16 

2)18  8)18^  2)20  4)20^  5)20^  3)21  2)22  2)24 

3)24^  4)24^  5)25^  8)27^  4)28^  3)30^  5)30  4)32^ 

8)33^  5)35^  8)36  4)36  4)40  5)40  4)44  5)45 

4)48^  5)50^  5)55  5)60^ 


50  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XCIL 

WRITTEN    WORK. 

SUM. 
1.       2.        3.       4.       5.       6.        7.       8.       9.      10. 


1 

2 

3 

4 

1 

1 

1 

2 

3 

2 

2 

1 

1 

1 

2 

3 

2 

1 

2 

4 

3 

1 

1 

2 

3 

2 

4 

3 

3 

2 

1 

2 

2 

1 

1 

2 

1 

2 

2 

4 

2 

2 

1 

2 

4 

4 

5 

5 

5 

5 

11. 

12. 

13. 

14. 

15. 

1(5. 

17. 

18. 

19. 

20. 

1 

2 

2 

3 

3 

3 

4 

4 

5 

5 

3 

3 

4 

4 

5 

4 

3 

4 

4 

4 

4 

4 

3 

2 

3 

5 

4 

3 

3 

5 

2 

3 

4 

3 

4 

6 

3 

3 

3 

4 

5 

5 

5 

5 

5 

4 

5 

5 

4 

4 

21. 

22. 

23. 

£4. 

25. 

2£. 

27. 

28. 

22. 

30. 

1 

2 

3 

4 

4 

4 

4 

4 

5 

5 

2 

4 

3 

3 

4 

4 

3 

5 

5 

4 

3 

3 

2 

1 

2 

5 

4 

4 

4 

5 

4 

2 

4 

5 

2 

3 

5 

5 

4 

4 

2 

1 

5 

3 

5 

3 

4 

4 

5 

5 

5 

4 

3 

3 

5 

5 

3 

5 

5 

4 

51. 

32. 

33. 

34. 

35. 

36. 

37. 

35. 

12 

21 

11 

22 

12 

13 

15 

24 

21 

12 

22 

33 

31 

22 

41 

32 

23 

32 

33 

11 

13 

14 

23 

15 

31 

13 

31 

13 

32 

41 

31 

51 

13 

81 

13 

31 

28 

32 

14 

24 

22 

32 

82 

12 

22 

23 

21 

38 

CHAPTER  ONE.  51 

LESSON    XCIII. 

SUM. 


1. 

2.     3. 

4. 

5. 

6. 

7.    8. 

52 

22    32 

22 

33 

40 

82    14 

25 

33    13 

11 

12 

15 

15    51 

34 

11    41 

54 

21 

23 

50    13 

12 

44    15 

83 

41 

31 

34    31 

21 

13    22 

21 

50 

42 

21    12 

38 

41    31 

12 

24 

35 

35    21 

22 

25    14 

55 

32 

22 

51    45 

9. 

10. 

11. 

12. 

13. 

14. 

123 
312 

213 
821 

323 
142 

523 
412 

253 
312 

812 
244 

231 

132 

821 

345 

411 

425 

142 

245 

532 

123 

135 

243 

234 

814 

225 

314 

522 

312 

143 

231 

345 

451 

248 

253 

315 

123 

321 

123 

451 

804 

253 

512 

543 

435 

824 

450 

15. 

16. 

17. 

18. 

19. 

20. 

421 

841 

415 

404 

811 

514 

243 

214 

230 

250 

133 

182 

824 

352 

354 

313 

223 

854 

152 

113 

113 

142 

415 

113 

413 

831 

821 

814 

152 

331 

302 

214 

214 

152 

314 

124 

243 

153 

142 

415 

142 

142 

324 

205 

323 

322 

818 

323 

153 

513 

454 

183 

250 

803 

413 

242 

803 

811 

404     454 

fTS'  IIH^''...^  T 

\  /v    oy   x  v 
A  f  riBmfslirV511 

52  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XCIV. 

SUM. 


1. 

2. 

3. 

4. 

6. 

1234 

4321 

5432 

3214 

2435 

2341 

8214 

4325 

2143 

5342 

3412 

2134 

3245 

1432 

3031 

4123 

1432 

2543 

4321 

1534 

1235 

5213 

1234 

3254 

4123 

2351 

2354 

4321 

4313 

3542 

6. 

7. 

8. 

9. 

10. 

3452 

2534 

3245 

4344 

5445 

2313 

3142 

4532 

5544 

4554 

3452 

4523 

2344 

3x54 

5454 

3214 

2134 

4321 

5543 

4545 

2543 

4943 

3245 

3445 

4444 

4231 

2532 

2321 

3534 

5555 

2435 

3144 

5454 

5443 

4545 

5232 

4522 

3232 

5334 

5454 

3424 

2333 

4114 

3445 

4545 

4332 

4455 

8553 

4835 

5454 

11. 

12. 

13. 

14. 

15. 

4352 

5324 

5334 

5484 

4444 

3243 

4343 

8552 

3252 

5555 

3421 

5215 

4235 

2313 

3334 

5253 

1453 

8421 

4258 

5435 

3445 

2532 

4345 

3534 

4553 

5345 

5344 

3254 

5234 

5435 

4534 

3423 

4523 

2453 

4354 

3452 

5254 

3254 

3333 

5444 

4325 

4545 

4554 

4444 

4555 

5433 

5334 

5555 

5555 

5555 

CHAPTER  ONE.  53 

LESSON    XCV. 

DIFFERENCE.-WRITTEN    WORK. 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

<5. 

P. 

10. 

23 

24 

32 

34 

42 

51 

52 

50 

52 

61 

12 

11 

14 

15 

23 

33 

35 

82 

34 

34 

11. 

12. 

13. 

14. 

15. 

18. 

17, 

18. 

19. 

20. 

62 

61 

61 

62 

70 

71 

73 

72 

63 

53 

23 

35 

85 

43 

43 

44 

45 

34 

35 

35 

21. 

£2. 

£3. 

£4. 

25. 

2& 

27. 

25. 

20, 

30. 

72 

71 

72 

73 

70 

81 

81 

80 

80 

82 

53 

23 

34 

25 

24 

22 

24 

35 

23 

23 

31. 

32. 

33. 

34. 

35. 

36. 

37. 

38. 

39. 

40. 

83 

83 

83 

83 

90 

90 

90 

90 

91 

91 

24 

35 

45 

54 

18 

22 

34 

43 

24 

15 

41. 

42. 

43. 

44. 

45. 

46. 

47. 

48. 

49. 

50. 

91 

91 

91 

91 

92 

92 

93 

93 

94 

94 

24 

42 

34 

43 

54 

45 

34 

44 

55 

45 

51. 

£2. 

53. 

54. 

55. 

56. 

57. 

58. 

101 

101 

102 

102 

103 

103 

104 

104 

43 

45 

34 

35 

44 

45 

45 

55 

54  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XCV'I. 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

9. 

321 

322 

423 

431 

522 

532 

523 

512 

132 

123 

234 

243 

234 

245 

245- 

254 

9. 

10. 

11. 

72. 

13. 

14. 

75. 

16. 

513 

622 

612 

632 

610 

613 

621 

602 

245 

344 

855 

444 

355 

454 

355 

335 

17. 

18. 

19. 

20. 

21. 

22. 

23. 

24. 

622 

621 

722 

712 

720 

713 

712 

711 

433 

435 

345 

434 

445 

545 

454 

544 

25. 

26. 

29. 

28. 

£0. 

30. 

'  31. 

52. 

722 

723 

714 

603 

921 

732 

720 

702 

555 

545 

325 

435 

455 

555 

354 

534 

33. 

34. 

35. 

5(5. 

37. 

55. 

52. 

40. 

811 

812 

821 

810 

801 

821 

832 

843 

433 

443 

844 

533 

533 

455 

554 

355 

41. 

42. 

45. 

44. 

45. 

46. 

47. 

45. 

912 

931 

921 

933 

943 

910 

902 

922 

453 

402 

414 

514 

454 

354 

448 

555 

CHAPTER  ONE.  55 

LESSON    XCVII. 


1. 

2. 

3. 

4. 

5. 

6. 

4321 

4321 

4312 

4112 

4032 

4203 

1244 

2424 

2413 

3453 

2513 

2314 

f. 

8. 

9. 

10. 

11. 

12. 

5201 

5350 

5102 

5213 

5321 

5324 

2324 

3455 

2343 

2454 

8453 

2435 

13. 

14. 

15. 

16. 

17. 

18. 

6204 

6032 

6213 

6121 

6321 

6083 

2461 

8345 

2845 

8254 

2434 

3524 

19. 

20. 

21. 

22. 

23. 

24. 

7210 

7111 

7212 

7130 

7213 

7101 

3245 

8344 

4325 

4335 

5134 

5434 

25. 

26. 

27. 

28. 

29. 

30. 

8121 

8211 

8122 

8102 

8230 

8322 

3242 

3452 

4844 

4834 

5345 

5544 

31. 

32. 

33. 

34. 

35. 

36. 

9211 

9121 

9213 

9304 

9280 

9321 

4354 

4354 

4345 

5432 

5345 

5544 

56  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XCVIII. 

ORAL  PROBLEMS. 

2.  A  farmer  sold  11  hogs  to  one  man  and  3  to  another. 
How  many  did  he  sell  to  both  ? 

2.  Gave  12  cents  for  marbles  and  4  cents  for  a  pencil. 
How  much  was  spent  for  both  ? 

3.  John  is  13  years  old  and  George  is  5  years  older.     How 
old  is  George  ? 

4.  James  earned  14  cents  and  his  father  gave  him  4  cents, 
fiow  many  cents  did  he  then  have? 

5.  Lucy  bought  16  oranges  and  Kittie  5  oranges.     How 
many  oranges  did  they  both  buy? 

6.  Sarah  ate  18  chestnuts  and  Jane  ate  4.     How  many 
did  they  both  eat? 

7.  Belle  is  15  years  old,  which  is  4  years  younger  than 
Blanche.     How  old  is  Blanche? 

8.  Kate  is  17  years  old.     How  old  will  she  be  in  5  years 
more? 

9.  A  boy  had  14  cents  and  wanted  5  cents  more  than  he 
had.     How  many  cents  did  he  want? 

10.  A  girl  having  19  chickens  lost  4  of  them  by  death.  How 
many  were  left? 

11.  Paid  21  cents  for  a  slate  and  5  cents  less  for  a  book. 
What  is  the  cost  of  the  book? 

12.  Charles  is  22  years  old,  which  is  4  years  older  than 
Lucy.     How  old  is  Lucy? 

13.  John  is  19  years  old.     How  old  was  he  5  years  ago? 

14.  A  man  having  $18  gave  $5  of  it  for  a  barrel  of  flour. 
How  much  was  left? 

15.  A  boy  carrying  two  dozen  eggs  broke  5  of  them.     How 
many  were  unbroken? 


CHAPTER  ONE.  57 

LESSON    XCIX. 

1.  If  you  had  22  cents,  which  is  4  cents  less  than  your 
friend  has,  how  many  cents  has  your  friend  ? 

2.  George  traveled  23  miles  and  Joe  5  miles  farther.     How 
far  did  Joe  travel  ? 

3.  Maggie  wrote  24  words,  which  was  4  less  than  the  num- 
ber Julia  wrote.     How  many  did  Julia  write  ? 

4.  Lucy  had  25  buttons  on  her  dress,  of  which  she  lost  8 
buttons.     How  many  were  left  ? 

5.  If  A  is  27  years  old  and  4  years  older  than  B,  how  old 
isB? 

6.  Mr.  Jones  is  24  years  old.     How  old  was  he  5  years  ago  ? 

7.  I  have  $27,  which  is  $4  less  than  I  had  yesterday.    How 
much  had  I  yesterday  ? 

8.  How  much  money  has  a  man  if  he  can  spend  $5  and 
have  $23  left? 

9.  How  many  marbles  has  a  boy,  if  when  he  receives  4 
more  he  has  29  marbles  ? 

10.  A  boy  bought  a  knife  for  28  cents  and  sold  it  for  5 
cents  more.     How  much  did  he  get  for  it  ? 

11.  I  have  a  book  that  cost  12  cents.      If  I  sell  it  at  a  loss 
of  4  cents,  how  much  do  I  get  for  it  ? 

12.  $34  was  paid  for  a  shawl,  which  is   $4  less  than  the 
cost  of  a  cloak.     What  is  the  cost  of  the  cloak  ? 

13.  An  article  is  sold  for  $33,  which  is  $4  more  than  the 
cost  of  it.     What  was  the  cost  of  it  ? 

14.  A  traveled  37  miles.     How  far  should  B  travel  to  make 
a  journey  4  miles  farther? 

15.  Bought  a  book  for  43  cents,  but  lacked  5  cents  of  hav- 
ing enough  money  to  pay  for  it.     How  much  money  had  I  ? 

16.  Mr.  B.  is  54  years  old,  which  is  5  years  older  than  his 
wife.     How  old  is  his  wife? 


58  FIRST  BaOK  IN  ARITHMETIC. 

LESSON    C. 

WRITTEN    PROBLEMS. 

1.  Bought  a  pound  of  coffee  for  28  cents  and  a  pound  of 
butter  for  25  cents.     What  is  the  cost  of  both  ? 

2.  James  earned  44  cents  one  day  and  52  cents  the  next. 
How  much  did  he  earn  in  both  days  ? 

3.  Bought  a  dress  for  $24,  a  shawl  for  $15,  and  a  cloak 
for  $14.     What  was  the  cost  of  all? 

4.  At  32  cents  a  pound,  how  much  more  does  a  pound  of 
coffee  cost  than  a  pound  of  sugar  at  12  cents  ? 

6.  John  had  a  fish  line  42  feet  long  and  cut  off  25  feet  of 
it  and  gave  it  to  his  brother.     How  much  was  left  ? 

6.  I  have  255  sheep  in  one  pasture,  234  in  another,  334  in 
another.     How  many  sheep  in  the  three  pastures  ? 

7.  A  dress  pattern  cost  $45,  the  trimmings  $14,  and  the 
making  of  it  $13.     What  was  the  cost  of  the  dress? 

8.  A  man  bought  a  watch  for  $40  and  sold  it  for  $63. 
How  much  was  gained? 

9.  A  farmer  sold  a  horse  for  $96,  which  is  $23  more  than 
the  cost.     How  much  was  the  cost  ? 

10.  A  lady  has  $87.     How  much  may  she  lose  and  yet 
have  $53? 

11.  Bought  a  horse  for  $135,  which  is  $45  less  than  I 
received  for  him.     What  was  the  selling  price  ? 

12.  Paid  $3452  for  a  house,  $425  for  painting  it,  and  $2312 
for  furniture.     How  much  was  the  entire  cost  ? 

13.  Paid  $6321  for  a  farm,  and  $2453  for  a  house.     How 
much  less  did  the  house  cost  than  the  farm  ? 

14.  Arthur  finds  234  nuts  under  one  tree,  303  under  another, 
and  54  under  another.     How  many  nuts  did  he  find  ? 

15.  Frank  finds  605  under  one  tree  and  234  under  another. 
How  many  more  were  found  under  one  tree  than  under  the 
other? 


CHAPTER  ONE.  59 

LESSON    CI. 

1.  Bought  8  car  loads  of  wheat,  paying  for  the  first  $245, 
for  the  second  $324,  and  for  the  third  $453.     How  much  was 
paid  for  all? 

2.  Paid  $628  for  wheat  and  $254  for  corn.     How  much 
more  was  paid  for  the  wheat  than  the  corn  ? 

3.  If  an  engine  travels  245  miles  each  day,  how  far  does  it 
travel  in  four  days? 

4.  A  gentleman  having  $831,  gave  over  to  his  son  $354. 
How  much  did  he  retain  ? 

5.  A  paid  $543  for  taxes,  B   $352,  and  C  $435.     How 
much  did  they  all  pay  ? 

6.  A  gentleman  is  53  years  old.     How  many  years  ago  was 
he  25  years  old  ? 

7.  A  farmer  has  $354.     How  much  more  does  he  need  that 
he  may  buy  a  field  worth  $912? 

8.  If  a  ship  sails  354  miles  each  day,  how  far  does  it  sail 
in  six  days-? 

9.  Bought  a  farm  for  $4553,  and  sold  it  for  $6310.     How 
much  was  gained? 

10.  Paid  $4326  for  a  house,  which  was  $3554  less  than 
the  cost  of  the  farm?     What  is  the  cost  of  the  farm? 

11.  A  man  has  $2355.     How  much  shall  he  add  to  it  to 
buy  a  farm  worth  $6304? 

12.  If  a  man  can  save  $542  each  year,  how  much  can  he 
save  in  six  years  ? 

13.  If  a  man  is  632  miles  from  Chicago,  and  travels  to- 
wards it  854  miles,  how  far  is  he  yet  from  Chicago? 

14.  How  many  palings  are  necessary  to  fence  a  square  lot 
if  each  side  requires  455  palings? 

15.  A  train  traveled  235  miles  in  one  day.     How  far  should 
it  travel  the  next  day  to  make  the  distance  510  miles  in  the 
two  days  ? 


60  FIRST  BOOK  IN  ARITHMETIC. 

LESSON     CII. 
PRODUCTS. 


1. 

& 

5. 

4. 

5. 

(5. 

7. 

321 

342 

234 

375 

543 

556 

654 

2 

2 

2 

2 

2 

2 

2 

8. 

P. 

10. 

11. 

12. 

75. 

74. 

572 

736 

896 

354 

465 

527 

654 

2 

2 

2 

3 

3 

3 

3 

15. 

16. 

17. 

18. 

IP. 

20. 

21. 

725 

853 

964 

973 

987 

998 

362 

3 

3 

3 

3 

3 

3 

3 

22. 

£5. 

£& 

25. 

26. 

27. 

& 

456 

463 

562 

578 

634 

675 

754 

4 

4 

4 

4 

4 

4 

4 

29. 

30. 

57. 

52. 

55. 

34. 

55. 

786 

893 

876 

889 

897 

965 

989 

4 

4 

4 

4 

4 

4 

4 

5(5. 

57. 

58. 

39. 

40. 

47. 

42. 

372 

389 

463 

482 

567 

598 

657 

5 

5 

5 

5 

5 

5 

5 

45. 

44. 

45. 

4tf. 

47. 

48. 

4P. 

694 

765 

789 

876 

885 

976 

987 

5 

5 

5 

5 

5 

5 

5 

CHAPTER  ONE.  61 

LESSON    CIII. 

PRODUCTS. 


1. 

£. 

3. 

4. 

5. 

6. 

1234 

3421 

5632 

4573 

6285 

7057 

2 

2 

2 

2 

2 

2 

7. 

5. 

9. 

10. 

11. 

72. 

5063 

6507 

7849 

8976 

3563 

4675 

2 

2 

2 

2 

3 

3 

13. 

14. 

15. 

16. 

17. 

18. 

5063 

6708 

7639 

7584 

8509 

8937 

3 

3 

3 

3 

3 

3 

IP. 

20. 

21. 

£& 

23. 

24. 

9086 

9098 

3671 

4563 

5675 

6307 

3 

3 

4 

4 

4 

4 

25. 

26. 

27. 

28. 

29. 

30. 

6895 

7086 

7609 

8058 

8607 

9368 

4 

4 

4 

4 

4 

4 

31. 

32. 

33. 

34. 

3S. 

36. 

9976 

3684 

4076 

5481 

6387 

6758 

4 

5 

5 

5 

5 

5 

37. 

38. 

39. 

40. 

41. 

42. 

7893 

7089 

8764 

8965 

9768 

9987 

5 

5 

5 

5 

5 

5 

62 


FIRST  BOOK  IN  ARITHMETIC. 


LESSON    CIV. 

LESSON   CV. 

How  many  are 
2  times  3354  peaches? 
2  times  5623  inches? 

How  many  are 
2  times  4682  pencils? 
2  times  6428  dollars? 

2  times  8706  melons? 

2  times  8640  bushels? 

3  times  4078  minutes? 

3  times  5397  acres? 

3  times  7186  gallons? 
3  times  9742  barrels? 

3  times  7539  letters? 
3  times  9375  blotters? 

4  times  5965  baskets? 

4  times  4268  boxes? 

4  times  7598  benches? 
4  times  9639  tables? 

4  times  6842  wagons? 
4  times  8624  kettles? 

5  times  4385  houses? 
5  times  6739  gallons? 
5  times  8096  ink-mills? 

5  times  5793  pictures? 
5  times  7395  figures? 
5  times  9537  oranges? 

LESSON     CVI. 


QUOTIENTS. 


1. 

S. 

3. 

4. 

5. 

6. 

-       7. 

2)26 

2)28 

2)42 

2)44 

2)46 

2)48 

2)62 

8. 

9. 

10. 

11. 

12. 

13. 

14. 

2)64 

2)66 

2)68 

2)80 

2)84 

2)86 

2)88 

15. 

16. 

17. 

is. 

19. 

20. 

21. 

3)39 

3)63 

3)66 

3)69 

3)93 

3)96 

3)99 

22. 

23. 

24. 

25. 

26. 

27. 

28. 

4)80 

4)84 

4)88 

4)480 

4)804 

5^550 

5)505 

CHAPTER  ONE.  63 
LESSON    CVIL 

QUOTIENTS. 

1.            2.            3.              4.            d.  6.  7. 

2)124       2(142       2)144       2)146       2)148  2)162  2)164 

8.             9.             10.            11.           12.  13.  14. 

2)166       2)168       2)182       2)184       2)186  2)188  2)180 

15.             16.           17.            18.           19.           20.  21. 

3)123       3)156       3)129       3)150       3)153  3)156  3)159 

22.             23.           24.             25.           26.           27.  28. 

3)180       3)183       3)186       3)189       3)210  3)216  3)219 

29.             30.           31.             32.           33.           34.  35. 

4)124       4)128       4)160       4)164       4)168  4)200  4)204 

36.            37.          38.             39.           40.           41.  42. 

4)208       4)244       4)248       4)284       4)283  4)324  4)328 

43.             44.           45.            46.           47.           48.  49. 

5)155       5)200       5)205       5)250       5)255  5)200  5)305 

50.             51.           52.             53.           54.           55.  56. 

5)350       5)355       5)400       5)405       5)455  5)500  5)505 


64  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    CVIIL 

QUOTIENTS. 

1.  2.      3.      4.  5.      6. 

2)1202  2)1404  2)1628   2)1846  2)1918  2)1812 

7.  8.      9.     10.  11.     12. 

2)2356  2)3878   2)4374  2)5638  2)6972  2)7856 

13.  14.     Id.     16.  17.     18. 

3)1206  3)1563   3)1896   3)2196  3)2436  3)2769 

19.  20.     21.     22.  23.     24. 

3)4527  3)5436   3)6318   3)6519  3)6816  3)7296 

25.  26.     27.     28.  29.     30. 

4)1249  4)1684   4)2088   4)2480  4)2848  4)3224 

31.  32.     33.     34.  35.     36. 

4)3748  4)4516   4)5648   4)6528  4)7280  4)8748 

37.  38.     39.     40.  41.     42. 

5)1505  5)2050   5)2515   5)3050  5)3505  5)4055 

43.  44.     45.     46.  47.     48. 

5)4525  5)5035   5)5520   5)6040  5)7745  5)9865 


LESSON    CXIX. 

What  is  £  of  246? 

SUGGESTION:    \  of  246  equals  2)246. 

What  is  \  of  352?     456?     572?     658?     7648?  8364? 

What  is  I  of  456?     579?     654?     768?     8460?  9576? 

What  is  \  of  468?     544?     672?     968?     8564?  9564? 

What  is     of  435?     570?     695?     780?     8655?  9750? 


CHAPTER  ONE. 


65 


LESSON  CX. 

How  many  times  are  : 
2  dollars  in  2146  dollars? 
2  peaches  in  4564  peaches? 

2  melons  in  6732  melons? 

3  acres  in  5625  acres? 

3  buttons  in  7566  buttons? 

3  plums  in  9765  plums? 

4  letters  in  5628  letters? 
4  miles  in  6976  miles? 

4  days  in  8796  days? 

5  rods  in  5925  rods? 

5  books  in  7830  books? 
5  berries  in  9715  berries? 


LESSON  CXI. 


What  is  l 
What  is  l 
What  is  i 
What  is  l 
What  is  -1 
What  is  1 
|  of  5624 
]-  of  7436 
l  of  9884 
-i  of  4625 
l  of  6780 
l  of  8575 


of  3428  dollars? 
of  5624  apples? 
of  7868  oranges? 
of  5868  lemons? 
of  7263  dates? 
of  9582  figs? 
hours  is  what? 
gallons  is  what? 
quarts  is  what? 
pecks  is  what? 
cans  is  what? 
cattle  is  what? 


LESSON  CXII. 

How  many  times 

2  horses  are  3154  horses? 
2  sheep  are  5784  sheep? 

2  pounds  are  6354  pounds? 

3  goats  are  7953  goats? 
3  nails  are  9735  nails? 

3  bushels  are  8262  bushels? 

4  dollars  are  6972  dollars? 
4  minutes  are  8764  minutes? 

4  chairs  are  9352  chairs? 

5  rails  are  7645  rails? 
5  rings  are  9760  rings? 

5  ounces  are  9975  ounces? 


LESSON  CXIII. 
How  many  times 
2  cents  are  7648  cents? 
2  oranges  are  9786  oranges? 

2  houses  are  8324  houses? 

3  cords  are  6585  cords? 

3  barrels  are  8763  barrels? 

3  miles  are  9765  miles? 

4  yards  are  7528  yards? 

4  inches  are  9876  inches? 

4  acres  are  8048  acres? 

5  children  are  6420  children  ? 
5  women  are  3545  women? 

-5  trunks  are  9680  trunks? 


66  FIRST  BOOK  IN  ARITHMETIC. 

LESSON     CXIV. 
ORAL    PROBLEMS. 

1.  If  one  lemon  cost  3  cents,  what  is  the  cost  of  2  lemons? 

2.  What  is  the  cost  of  2  oranges  at  4  cents  each? 

3.  At  5  cents  a  yard,  what  is  the  cost  of  2  yards  of  tape? 

4.  What  is  the  cost  of  2  pencils  at  6  cents  each? 

5.  At  3  dollars  a  day,  how  much  can  a  man  earn  in  3  days? 

6.  If  1  gallon  equals  4  quarts,  how  many  quarts  do  3  gal- 
lons equal? 

7.  What  is  the  cost  of  3  tops,  if  1  top  costs  5  cents? 

8.  At  $6  a  ton,  what  is  the  cost  of  3  tons  of  coal? 

9.  If  A  has  3  apples  and  B  4  times  as  many,  how  many 
hasB? 

10.  At  $4  a  yard,  what  is  the  cost  of  4  yards  of  cloth? 

11.  At  5  cents  a  yard,  what  is  the  cost  of  5  yards  of  tape? 

12.  How  many  eggs  are  in  4  nests,  if  there  are  6  eggs  in 
each  nest? 

13.  What  is  the  cost  of  5  pairs  of  shoes  at  $3  a  pair? 

14.  James  is  4  years  old  and  John  5  times  as  old,  how  old  is 
John? 

15.  At  5  cents  each,  what  is  the  cost  of  5  pencils? 

16.  What  is  the  cost  of  5  hats  at  $6  each? 

17.  If  ^  of  a  yard  of  tape  costs  4  cents,  what  is  the  cost  of 
1  yard? 

18.  What  is  the  cost  of  1  ton  of  coal,  if  J  of  a  ton  costs  $4? 

19.  If  ^  of  a  melon  costs  5  cents,  what  is  the  cost  of  1 
melon? 

20.  How  old  is  Mary,  if  \  of  her  age  is  7  years? 

21.  What  is  the  cost  of  2  yards  of  ribbon  if  one  yard  cost 
6  cents? 

22.  If  one  pencil  costs  7  cents,  what  is  the  cost  of  2  pencils? 

23.  What  is  the  cost  of  2  melons  if  one  melon  cost  8  cents? 


CHAPTER  ONE.  67 

LESSON     CXV. 


1 .  If  one  bunch  of  grapes  is  worth  9  cents,  what  is  the  cost 
of  2  bunches? 

2.  How  far  can  a  man  travel  in  3  hours  if  he  can  travel  7 
miles  in  one  hour? 

3.  How  many  yards  are  there  in  3  pieces  of  cloth  if  there 
are  8  yards  in  each  piece? 

4.  If  3  men  can  do  a  piece  of  work  in  9  days,  in  what  time 
can  one  man  do  it? 

5.  If  a  boy  can  walk  12  miles  each  day,  how  far  can  he 
walk  in  3  days? 

6.  What  is  the  cost  of  4  yards  of  cotton  cloth,  if  one  yard 
costs  7  cents? 

7.  A  boy  has  8  apples  and  4  times  as  many  peaches.    How 
many  peaches  has  he? 

8.  What  is  the  cost  of  4  quarts  of  oil,  if  one  quart  cost  9 
cents? 

9.  If  4  men  can  mow  a  field  of  grass  in  12  days,  in  how 
many  days  can  one  man  mow  it? 

10.  If  one  melon  is  worth  7  peaches,  how  many  peaches 
are  5  melons  worth? 

11.  If  a  man  travels  from  his  home  8  miles  an  hour,  how 
far  away  will  he  be  in  5  hours? 

12.  Mary  has  5  flocks  of  chickens  and  9  chickens  in  each 
flock.     How  many  chickens  has  she? 

13.  If  one  pair  of  boots  cost  $12,  what  is  the  cost  of  5 
pairs? 

14.  At  2  cents  each  how  many  tops  cost  4  cents? 

15.  At  2  dimes  each  how  many  slates  cost  6  dimes? 

16.  If  2  apples  cost  8  cents,  what  is  the  cost  of  1  apple? 

17.  How  many  lemons  cost  10  cents,  at  2  cents  each? 

18.  If  2  tons  of  coal  cost  $12,  what  is  the  cost  of  1  ton? 


68  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    CX VI. 


1.  At  3  miles  an  hour,  in  what  time  can  a  man  walk  6 
miles  ? 

2.  At  $3  a  day,  in  what  time  can- a  man  earn  $9. 

3.  If  3  hats  cost  $12,  what  is  the  cost  of  1  hat? 

4.  How  many  oranges  cost  15  cents,  at  3  cents  each? 

5.  If  3  sheep  cost  $18,  what  is  the  cost  of  1  sheep? 

6.  At  4  cents  each,  how  many  oranges  cost  8  cents? 

7.  At  $4  a  day,  in  what  time  can  a  man  earn  $12? 

8.  If  4  oranges  cost  16  cents,  what  is  the  cost  of  1  orange? 

9.  How  many  pencils  at  4  cents  each  can  he  bought  for 
28  cents? 

10.  If  4  men  mow  24  acres  of  grass,  how  much  does  1  man 
mow? 

11:  At  $5  a  ton,  how  many  tons  of  coal  cost  $10? 

12.  How  many  bottles  cost  15  cents  if  1  bottle  cost  5  cents? 

13.  If  5  caps  cost  $20,  what  is  the  cost  of  1  cap? 

14.  How  many  nickels  equal  25  cents,  if  1  nickel  equals  5 
cents? 

15.  If  1  man  digs  a  ditch  in  30  days,  in  what  time  can  5 
men  dig  it? 

16.  At  $2  a  bushel,  how  many  bushels  of  wheat  can  be 
bought  for  $14? 

17.  If  4  melons  cost  32  cents,  what  is  the  cost  of  1  melon? 

18.  How  many  cords  of  wood  can  be  bought  for  $36,  if  1 
cord  costs  $4? 

19.  What  is  the  cost  of  1  slate,  if  5  slates  cost  45  cents? 

20.  At  4  cents  each,  how  many  pencils  can  be  bought  for 
48  cents? 

21.  If  5  tons  of  coal  cost  $45,  what  is  the  cost  of  1  ton? 

22.  How  many  vests  at  $5  each  can  be  bought  for  $60? 


CHAPTER  ONE.  69 

LESSON    CXVII. 

WRITTEN    PROBLEMS. 

1.  If  1  horse  cost  $  124,  what  is  the  cost  of  2  horses? 

2.  How  far  does  a  vessel  sail  in  2  days,  if  it  sails  214  miles 
each  day? 

3.  At  $  143  an  acre,  what  is  the  cost  of  2  acres  of  ground? 

4.  How  much  can  a  man  earn  in  2  months,  if  he  earns 
|132  each  month? 

5.  A  merchant  sold  125  barrels  of  flour  one  day  and  three 
times  as  many  the  next.     How  much  did  he  sell  the  next  day? 

6.  A  owns  231  acres  of  land  and  B  3  times  as  much.    How 
much  does  B  own? 

7.  From  B  to  C  it  is  321  miles,  and  3  times  as  far  from  B 
to  D.     How  far  is  it  from  B  to  D. 

8.  John  has  $231  and  James  has  3  times  as  much.     How 
much  has  James? 

9.  If  an  engine  runs  324  miles  in  one  day,  how  far  does  it 
run  in  4  days? 

10.  The  rent  of  a  house  for  1  year  is  $234,  what  is  the  rent 
of  4  such  houses? 

11.  Mr.  A.  saves  $432  each  year.     How  much  does  he 
save  in'  4  years? 

12.  What  is  the  cost  of  4  carriages,  if  each  carriage  costs 
$243? 

13.  What  is  the  cost  of  5  acres  of  ground,  if  1  acre  costs 
$243? 

14.  A  tourist  traveled  325  miles  one  week,  and  5  times  as 
far  the  next.     How  far  did  he  travel  the  second  week? 

15.  A's  wages  are  $435  each  month.     What  are  his  wages 
for  5  months? 

16.  B  invested  $524  in  stocks  and  C  5  times  as  much. 
How  much  did  C  invest? 


70  FIRST  BOOK  IN  ARITHMETIC. 

LESSON     CXVIII. 

1.  If  an  acre  lot  is  worth  $435,  what  are  2  such  lots  worth? 

2.  If  ^  an  acre  lot  is  worth  $356,  what  is  1  acre  lot  worth? 

3.  At  $436  each,  what  is  the  cost  of  2  fine  sleighs? 

4.  If  |  the  rent  of  a  house  for  a  year  is  $364,  what  is  the 
whole  rent  worth? 

5.  At  $543  dollars  each,  what  is  the  value  of  3  loads  of 
wheat? 

6.  What  is  the  cost  of  a  house,  if  J  of  the  cost  is  $545? 

7.  What  is  the  cost  of  3  pianos,  if  1  piano  cost  $654? 

8.  If  a  ship  sail  654  miles  in  J  of  a  week,  how  far  does  it 
sail  in  1  week? 

9.  If  a  mill  will  grind  756  barrels  of  flour  each  day,  how 
many  barrels  of  flour  will  it  grind  in  4  days? 

10.  How  much  money  has  Mr.  A.  if  ^  of  his  money  equals 
$764? 

11.  What  is  the  value  of  4  notes,  if  each  note  is  worth  875? 

12.  If  £  of  a  merchant's  goods  is  worth  $890,  what  are  the 
goods  worth? 

13.  What  is  the  expense  of  running  a  mill  5  days,  if  it  cost 
$695  to  run  it  one  day? 

14.  If  -J  of  the  cost  of  a  house  and  lot  is  $786,  what  is  the 
whole  cost? 

15.  What  is  the  cost  of  building  5  barns,  if  each  barn  cost 
$986? 

16.  What  is  the  cost  of  building  a  house,  if  |  of  the  cost 
is  $999? 


CHAPTER  ONE.  71 

LESSON    CXIX. 

1.  At  $2  a  bushel  how  many  bushels  of  wheat  can  be 
bought  for  $154? 

2.  If  2  horses  are  worth  $258,  what  is  each  horse  worth? 
5.  How  many  acres  of  government  land  can  be  bought  for 

$296,  if  one  acre  costs  $2? 

4.  What  is  the  cost  of  1  carriage  if  2  carriages  are  worth 
$472? 

5.  At  $3  a  day  in  what  time  can  a  man  earn  $675? 

6.  If  1  car  holds  465  bushels  of  coal,  how  much  does  £  of 
a  car  hold? 

7.  If  a  man  walk  3  miles  an  hour,  in  what  time  can  he  walk 
852  miles? 

8.  How  many  pages  are  there  in  1  book,  if  there  are  375  in 
3  books  of  the  same  size? 

9.  At  $4  a  yard,  how  many  yards  of  cloth  can  be  bought 
for  $2752? 

10.  If  4  yoke  of  oxen  cost  $3464,  what  is  the  cost  of  1  yoke? 

11.  Since  4  quarts  equal  1  gallon,  how  many  gallons  do 
8736  quarts  equal? 

12.  If  it  costs  $4516  to  pave  4  sidewalks,  what  is  the  cost 
of  paving  1  sidewalk? 

IS.  At  $5  a  share,  how  many  shares  of  stock  can  be  bought 
for  $2965? 

14.  If  a  house  cost  $3940,  what  is  the  -J-  of  the  cost? 

15.  How  many  cords  of  wood  at  $5  a  cord  can  be  bought 
for  $2352? 

16.  If    5   cottages   cost   $4875,  what  is  the  cost  of  each 
cottage? 

17.  If  a  merchant  saves  $395  in  five  years,  how  much 
does  he  save  each  year? 


72  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    CXX. 

1.  If  a  boy  connts  2  cents  each  second,  in  what  time  can 
he  count  534  cents? 

2.  If  2  city  lots  cost  $1978,  what  is  the  cost  of  one  lot? 

3.  In  how  many  days  can  a  man  save  $2350  if  he  saves  $2 
each  day? 

4.  How  many  bricks  can  one  mason  lay  a  day,  if  2  masons 
can  lay  5768  bricks? 

6.  How  many  bags,  each  holding  3  bushels,  can  be  filled 
from  5769  bushels  of  wheat? 

6.  If  3  horses  eat  2265  pounds  of  hay  in  1  month,  how 
much  does  1  horse  eat? 

7.  Mr.  B  paid  $6342  for  government  land  at  $3  an  acre. 
How  much  land  did  he  buy? 

8.  If  a  boat  is  worth  $7353,  what  is  J  of  its  value? 

9.  How  many  sheets  of  paper  are  required  for  5348  pages, 
if  one  sheet  equals  4  pages? 

10.  If  4  men  equally  own  a  boat  worth  $6532,  what  is  the 
value  of  each  man's  share? 

11.  If  4  yards  of  cloth  is  enough  for  1  suit,  7524  yards  is 
enough  for  how  many  suits? 

12.  If  8368  bricks  are  laid  in  a  wall,  how  many  are  laid  in 
\  of  the  wall? 

13.  At  5  pounds  each  can,  how  many  cans  can  be  filled 
from  7320  pounds  of  meat? 

14.  If  5  men  equally  share  8475  acres  of  land,  how  much 
does  each  one  own? 

15.  At  $5  per  mile  how  many  miles  of   railroad  can  be 
watched  for  $9320? 

16.  If  it  cost  $9875  to  build  1  mile  of  railroad,  what  is  the 
cost  of  building  -J-  of  a  mile? 


CHAPTER   II. 


In  adding  equal  numbers  of  the  same  kind,  certain  results 
or  facts  are  obtained,  which  form  the  basis  of  what  is  known 
as  multiplication.  These  facts  must  be  learned,  that  is,  mem- 
orized by  the  child,  and  when  so  learned  he  is  said  to  know 
the  multiplication  tables. 

To  learn,  then,  the  so-called  multiplication  tables,  is  to 
memorize  certain  results  of  addition.  It  has  been  deemed 
expedient  that  such  results  should  be  memorized  as  far  as 
twelve  12's. 

The  following  lessons  are  designed  to  show 

First ,  The  facts  to  be  memorized: 

6,  12,  18; 

7,  14,  21; 
9,                      18,                      27; 

8,  16,  24; 
12,                       24,  36;  etc. 

Second,  To  present  such  questions  and  examples  as  shall 
best  aid  the  memory  to  do  its  perfect  work. 


74  FIRST  BOOK  IN  ARITHMETIC. 

LESSON     I. 

6  30  54 

12  36  60 

18  42  66 

24  48  72 


a.  How  many  6's  in  12?    18?    24?    30?     86?    42?     48? 
64?     60?     66?     72? 

b.  What  is  1  of  12  ?    18?    24?    30?    36?    42?    48?    54? 
60?    66?    72? 

C.  What  part  of  6isl?  Of  12  is    2?  Of  18  is    3? 

Of  24  is    4?       Of  30  is  5?  Of  36  is    6?  Of  42  is    7? 

Of  48  is    8?       Of  54  is  9?  Of  60  is  10?  Of  66  is  11? 
Of  72  is  12? 

d.  2  is  I  of  what  number?    3?    4?    5?    6?    7?     8?     9? 
10?     11?     12? 


1.  If  a  barrel1  of  flour  cost  $6,  what  part  of  a  barrel  can 
be  bought  f or  $1?     $2?     $3?     $4     $5? 

2.  What  part  of  $6  is  $1?     $2?     $3?     $4?     $5? 

3.  What  is  ±  of  12?    f?    f?     £?    f? 

4.  What  is  1  of  18?     f?     f?     -|?     f? 

5.  What  is  i  of  24?     f?     f?     |?     |? 

6.  What  is  -J  of  36?    f  ?    |?    -f  ?    f  ? 

7.  What  is  ^  of  42?    f  ?     |?     f  ?    f  ? 
5.  What  is  |- of  48?    f?     f?     f?     f? 

9.    I  of  12  inches?     60  seconds?     24  hours?     18  quarts? 

10.  I  of  $54?         48  cents?         72  dimes?         30  nickels? 

11.  1  of  36  rods?     42  bushels?     66  marbles?     48  weeks? 


CHAPTER   TWO. 


75 


LESSON    II. 


18  equals  how  many  6's? 
54  equals  how  many  6's? 
66  equals  how  many  6's? 
48  equals  how  many  6's? 
42  equals  how  many  6's? 

5  equals  ^  of  what? 

11  equals  -^  of  what? 

8  equals  \  of  what? 

7  equals  \  of  what? 

8  equals  \  of  what? 


|  of  12  equals  what? 
|  of  42  equals  what? 
\  of  72  equals  what? 
\  of  24  equals  what? 
\  of  54  equals  what? 

\  of  what  equals  9  ? 
•J  of  what  equals  7  ? 
J  of  what  equals  11  ? 
\  of  what  equals  8  ? 
|  of  what  equals  12  ? 


19  equals  how  many  6's?      27  equals  how  many  6's? 

SUGGESTION:    19=6+6+6+1.         .-.  19=three  6's  and  1. 
27=6+6+64-6+3.    .-.  27=four  6's  and  3. 


20  is  how  many  6's? 
83  is  how  many  6's? 
40  is  how  many  6's? 
43  is  how  many  6's? 
47  is  how  many  6's? 
56  is  how  many  6's? 
65  is  how  many  6's? 
75  is  how  many  6's? 

How  many  6's  in  19? 
How  many  6's  in  27? 
How  many  6's  in  34? 
How  many  6's  in  39? 
How  many  6's  in  45? 
How  many  6's  in  59? 
How  many  6's  in  68? 
How  many  6's  in  78? 

\  of  18  is  how  many  1's? 
j-  of  36  is  how  many  3's? 
•J-  of  48  is  how  many  4's? 
\  of  60  is  how  many  5's? 


\  of  24  is  how  many  2's? 
J  of  42  is  how  many  1's? 
*  of  54  is  how  many  8's? 
\  of  72  is  how  many  6's? 


76  FIRST  BOOK  IN  ARITHMETIC. 

LESSON     III. 

1:  What  do  5  oranges  cost  at  6  cents  apiece? 

2.  What  will  9  sheep  cost  at  $6  a  head? 

3.  When  you  have  6  lessons  each  day,  how  many  lessons 
do  you  have  in  5  days? 

4.  What  is  the  cost  of  a  dozen  boxes  of  matches  at  6  cents 
a  box? 

5.  A  man  works  6  days  in  each  week.     How  many  days 
deos  he  work  in  7  weeks?     In  4  weeks?    In  8  weeks? 

6.  If  7  men  can  do  a  piece  of  work  in  6  days,  how  long 
will  it  take  one  man  to  do  it? 

7.  What  do  11  barrels  of  pork  cost  at  $6  a  barrel? 

8.  If  10  men  can  build  a  wall  in  6  days,  in  how  many  days 
can  one  man  do  it? 

9.  How  many  miles  can  a  man  walk  in  6  hours,  at  the 
rate  of  6  miles  an  hour? 

10.  If  the  interest  of  f  1  is  6  cents,  what  is  the  interest  of 
$10? 

11.  Cost  of  10  barrels  of  flour  at  $6  a  barrel? 

12.  Cost  of  20  sheep  at  $6  a  head? 

13.  Cost  of  planting  30  trees  at  $6  each? 

14.  Cost  of  40  slates  at  6  cents  apiece  ? 

15.  At  $50  a  month,  what  does  a  clerk  earn  in  six  months  ? 

16.  How  many  Ibs.  of  sugar  in  6  tubs  of  60  Ibs.  each  ? 

17.  How  many  Ibs.  of  cheese  are  there  in  six  cheeses,  each 
weighing  70  Ibs.  ? 

18.  As  many  dollars  were  paid  for  a  ton  of  hay  as  there 
are  6's  in  84.     What  was  the  cost  of  the  hay  ? 

19.  How  many  cents  are  there  in  6  dollars? 

20.  How  many  cents  are  there  in  60  dimes  ? 


CHAPTER  TWO.  77 

LESSON    IV. 

1.  At  $6  a  barrel  for  flour,  how  many  barrels  can  be 
bought  for  $36?     $42?     $60?     $72? 

2.  When  6  barrels  of  flour  cost  $36,  what  is  the  price  of 
one  barrel? 

SUGGESTION.  At  $6  a  barrel  as  many  ban-els  can  be  bought  for 
$36  as  there  are  6's  in  36.  36  equals  six  6's.  Therefore  6  barrels 
can  be  bought, 

When  6  barrels  of  flour  cost  $36  one  barrel  costs  one -sixth  of 
$36,  or  $6. 

3.  At  6  cents  a  quart  how  many  quarts  of  oil  can  be  bought 
for  54  cents? 

4.  When  6  quarts  of  oil  cost  30  cents,  what  is  the  price  per 
quart? 

5.  There  are  48  trees  in  6  equal  rows.     How  many  trees  in 
each  row? 

6.  In  an  orchard  the  trees  are  planted  in  rows.     There  are 
6  trees  in  each  row.     How  many  rows  must  there  be  to  con- 
tain 24  trees?     60  trees?     54  trees?     30  trees? 

7.  The  interest  of  $6  is  42  cents.     Interest  of  $1? 

8.  In  6  windows  there  are  36  panes  of  glass.     How  many 
panes  in  each  window? 

9.  If  a  man  walk  6  miles  an  hour,  in  how  many  hours  can 
he  walk  24  miles?     72  miles?     60  miles? 

10.  At  6  cents  apiece,  how  many  drawing  pencils  can  be 
bought  for  54  cents?     48  cents?     66  cents? 

11.  What  is  the  cost  of  J  of  a  ton  of  hay,  when  hay  is 
selling  at  $18  a  ton? 

12.  Cost  of  \  of  a  bbl.  of  flour  at  $9  a  barrel? 

13.  At  $120  for  6  calves,  what  is  the  cost  of  one? 

14.  There  are  6  working  days  in  a  week.     How  many  weeks 
in  42  working  days  ?     420  ?     36  ?     360  ?     54  ?     540  ? 

15.  If  for  $1  you  can  buy  6  yards  of  muslin,  what  will  12 
yds.  cost  ?     18  yds.  ?    24  yds.  ?    30  yds.  ?     42  yds.  ? 


78 


FIRST  BOOK  IN  ARITHMETIC. 


LESSON    V. 

7  35 

14  42 

21  49 

28  56 


63 
70 

77 
84 


a.  How  many  7's  in  14? 
63?     70?     77?     84? 


21?     28?     35?     42?    49?    56? 


b.  What  is  }  of  14? 
70?     77?     84? 


21?    28?    35?    42?    49?    56?    63? 


c.  What  part  of     7  is  1? 
Of  28  is    4?       Of  35  is  5? 
Of  56  is    8?       Of  63  is  9? 
Of  84  is  12? 

d.  2  is  <f  of  what  number? 
10?     11?     12? 


14  equals  how  many  7's? 
28  equals  how  many  7's? 
42  equals  how  many  7's? 
63  equals  how  many  7's? 

f  of  70  equals  what? 
\  of  42  equals  what? 
\  of  84  equals  what? 
ij-  of  35  equals  what? 

5  equals  ^  of  what? 
7  equals  -£  of  what? 
4  equals  ^  of  what? 
1  equals  $  of  what? 


Of  14  is  2? 
Of  42  is  6? 
Of  70  is  10? 


Of  21  is  3? 
Of  49  is  7? 
Of  77  is  11? 


3?     4?     5?    6?    7?    8?     9? 


56  equals  how  many  7's? 
85  equals  how  many  7's? 
84  equals  how  many  7's? 
49  equals  how  many  7's? 

\  of  77  equals  what? 
•f  of  28  equals  what? 
\  of  63  equals  what? 
Y  of  49  equals  what? 

3  equals  -£  of  what? 
6  equals  y  of  what? 
9  equals  \  of  what? 
8  equals  j  of  what? 


CHAPTER   TWO.  79 

LESSON    VI. 

1.  \  of  14  bushels?      21  books?      35  slates?      63  gallons? 

2.  \  of  $49?    70  cents?     56  years?     28  horses?    7  cups? 
5.  \  of  70  feet?  84  feet?          91  feet?          77  feet? 

4.  ^  of  140  pecks?  210  quarts?  350  pints? 

5.  There  are  7  days  in  a  week.     What  part  of  a  week  is  1 
day?     2  days?     3  days?     4  days?     5  days?     6  days? 

6.  What  is  |  of    7  days?  f?     fS      f?     f?     |? 

7.  What  is  $  of  14  hours?          f?      f-?      f?     f?      f? 

8.  What  is  -J  of  35  weeks?         f?     f?      f?      f?     f? 
P.  What  is  |  of  63  months?       f?     f?     f?     f?      f? 

10.  What  is  |  of  21  years?  f?  f?  f?  -f  ?  f? 

17.  What  is  \  of  28  cents?  f?  f?  f?  f?  f? 

7,2.  What  is  \  of  42  oranges  ?  f  ?  f  ?  f  ?  f  ?  f  ? 

15.  What  is  |  of  49  pears?  ??  f?  f?  f?  f? 

74.  What  is  ^  of  56  peaches?      f  ?      f  ?      f  ?      f  ?     -f  ? 

75.  How  many  7's  in  15?     19?     23?     27?     29?     32? 

16.  How  many  7's  in  20?     30?     40?     50?     60?     80? 

17.  How  many  7's  in  22?    31?     38?     46?     51?     53? 

18.  How  many  7's  in  13?     41?     62?     83?     47?     55? 

19.  How  many  7's  in  75?     78?     85?     90?     75?     98? 

20.  How  many  7's  in  280?    630?     560?     490?     140? 


80  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    VII. 

1.  What  will  5  barrels  of  flour  cost  at  $7  a  barrel? 

2.  How  many  days  are  there  in  4  weeks  ?     7  weeks  ? 

3.  With  7  desks  in  each  row,  how  many  desks  in  a  room 
with  8  rows?     9  rows  ? 

4.  At  $7  a  head,  what  will  6  sheep  cost? 

5.  At  7  cents  a  quart,  what  will  9  quarts  of  milk  cost? 

6.  8  boys  have  7  marbles  each.     How  many  marbles  does 
that  make? 

7.  9  girls  have,  each,  a  jumping  rope  7  feet  long.     What  is 
the  length  of  the  9  ropes? 

8.  What  cost  6  tons  of  hay  at  $7  a  ton? 

9.  If  a  boy  pick  7  quarts  of  cherries  in  an  hour,  how  many 
quarts  can  he  pick  from  8  o'clock  till  noon? 

10.  In  a  certain  school  there  are  12  benches.     On  each 
bench  there  are  7  boys.     How  many  boys  in  the  school? 

11.  At  $7  each,  how  many  sheep  will  $56  buy? 

12.  At  $56  for  7  sheep,  what  is  the  price  of  one  sheep? 

13.  Paid  84  cents  for  7  dozen  eggs.     Price  per  dozen? 

14.  John  has  56  cents.     His  sister  has  \  as  many.     How 
many  have  both  ? 

15.  Charles  has  \  of  28  cents,  and  Mary  has  |  of  35  cents. 
How  many  more  cents  has  Mary  than  Charles? 

16.  At  the  rate  of  7  miles  an  hour,  in  how  many  hours  can 
a  man  walk  49  miles?     63  miles?     56  miles?     21  miles? 

17.  A  man  works  7  hours  each  day.     How  many  days  will 
he  require  to  do  77  hours'  work  ?     84  hours'  work  ? 

18.  If  you  pay  63  cents  for  a  7-mile  ride,  what  is  the  price 
per  mile? 

19.  Paid  $42  for  wood  at  $7  a  cord.     How  many  cords 
were  purchased? 

20.  If  7  men  can  pave  a  block  in  10  days,  how  many  men 
would  it  take  to  do  the  same  work  in  1  day? 


CHAPTER  TWO. 


81 


LESSON  VIII. 

8                              40  72 

16                              48  80 

24                              56  88 

32                              64  96 


a.  How  many  8's  in  16?    24?    32?    40?    48?    56?    64? 

72?     80?    88?     96? 


b.  What  is  \  of  8? 
72?    80?    88?    96? 


16?    24?    32?    40?    48?     56?    64? 


C.  What  part  of  8  is  1? 
Of  32  is  4?  Of  40  is  5? 
Of  72  is  9? 

d.  2  is  |  of  what  number? 
10?     11?     12? 

40  equals  how  many  8's? 
56  equals  how  many  8's? 
72  equals  how  many  8's? 
24  equals  how  many  8's? 
96  equals  how  many  8's? 

|  of  8  equals  what? 
g  of  32  equals  what? 
\  of  48  equals  what? 
I  of  64  equals  what? 
|  of  40  equals  what? 

8  equals  |  of  what? 
7  equals  -|  of  what? 
6  equals  \  of  what? 
5  equals  J  of  what? 


Of  16  is  2? 

Of  48  is  6? 


Of  24  is  3? 
Of  56  is  7? 


3?     4?     5     6?     7?     8?    9? 

48  equals  how  many  8's? 
88  equals  how  many  8's? 
32  equals  how  many  8's? 
16  equals  how  many  8's? 
64  equals  how  many  8's? 

|  of  80  equals  what? 
^  of  72  equals  what? 
|  of  96  equals  what? 
|  of  16  equals  what? 
•1  of  88  equals  what? 

9  equals  -J  of  what? 
12  equals  J  of  what? 

4  equals  -|  of  what? 
10  equals  |  of  what? 


82 


FIRST  BOOK  IN  ARITHMETIC. 


LESSON     IX. 


1.    4  of  24  hours?        16  weeks?        64  desks?         $160? 


2.    I  of  $48?         $72?         56  dimes? 


40  bushels? 


f« 


t« 


.22 

8  • 

-22 
8  • 


f« 

53 

Q     • 


3.  |  of  96  dozen?       80  boxes?       32  quarts?       88  cows? 

4.  There  are  8  quarts  in  a  peck.     What  part  of  a  peck  is  1 
quart?    2  quarts?    3  quarts?    4  quarts?    5  quarts?    6  quarts? 
7  quarts? 

5.  1  quart  is  what  part  of  a  peck?     2  quarts?     3  quarts? 
4  quarts?     5  quarts?     6  quarts?     7  quarts? 

6.  What  is  |  of  16  dollars  ?     I  ?     I  ?     *  ? 

7.  What  is  l  of  40  dimes? 

8.  What  is  \  of  48  cents? 
P.  What  is  I  of  32  quarts? 

10.  What  is  I  of  56  quarts? 

11.  What  is  I  of  72  yards? 

12.  What  is  |  of  96  hats? 

13.  How  many  8's  in  17?    18?    20? 

26?  28? 

44?  54? 

46?  58? 

82?  89? 


1? 

|?  |?  | 

42  5£  .61 

O     •  O     •  O      ' 


fl 


14.  How  many  8's  in  25? 

15.  How  many  8's  in  34? 

16.  How  many  8's  in  36? 

17.  How  many  8's  in  75? 

18.  How  many  8's  in  160? 


240? 


8' 

f? 

f  • 

1? 

23? 

1? 
15? 

19? 

30? 

33? 

29? 

65? 

36? 

63? 

68? 

35? 

47? 

95? 

19? 

91? 

)?  320? 

720? 

LESSON    X. 

1.  At  $8  a  month,  how  much  can  a  boy  earn  in  6  months? 

2.  At  8  cents  a  quart,  what  do  3  quarts  of  strawberries  cost? 

3.  A  spider  has  8  legs.     How  many  legs  have  4  spiders? 
7  spiders? 


CHAPTER  TWO.  83 

4.  There  are  8  quarts  in  a  peck.     How  many  quarts  in  2 
pecks?     3  pecks?     5  pecks?     10  pecks?     12  pecks? 

5.  At  $8  a  ton,  what  will  3  tons  of  coal  cost?     4  tons? 
6  tons?     8  tons? 

6.  Cost  of  a  dozen  slates  at  8  cents  each? 

7.  How  many  miles  does  a  man  walk  in  9  days  when  he 
walks  8  miles  daily? 

8.  A  boy  saves  8  cents  a  day  by  selling  papers.    How  much 
money  does  he  save  in  a  week? 

.9.  If  8  men  do  some  work  in  5  days,  how  many  men  can 
do  the  same  work  in  1  day? 

10.  If  it  requires  8  yards  of  calico  to  make  a  gown,  how 
many  yards  will  be  required  to  make  7  such  gowns? 

11.  How  many  yards  of  velvet  can  be  bought  for  $48  at 
$8  a  yard? 

12.  If  8  yards  of  velvet  cost  $48,  what  is  the  cost  of  1  yard? 

13.  At  8  cents  a  pound  for  sugar,  how  many  pounds  will  72 
cents  buy? 

14.  How  many  barrels  of  flour  will  $96  purchase  at  $8  per 
barrel? 

15.  In  how  many  days  can  8  men  earn  as  much  as  4  men  in 
6  days? 

16.  48  cents  were  paid  for  coffee,  and  |-  as  much  for  sugar. 
How  much  was  paid  for  both? 

17.  How  many  pecks  in  16  quarts?   24  quarts?   32  quarts? 
56  quarts? 

18.  A  quantity  of  provision  will  last  1  man  80  days.     How 
long  will  it  last  8  men  ? 

19.  How  long  will  it  take  a  man  to  walk  72  miles  if  he  walks 
8  miles  each  hour? 

20.  For  $56  how  many  barrels  of  pork  can  be  bought  when 
$8  are  paid  for  1  barrel? 


84 


FIRST  BOOK  IN  ARITHMETIC. 


LESSON  XI. 

9            45  81 

18             54  90 

27             63  99 

36             72  108 

a.  How  many  9's  in  18?  27?  36?  45?   54?   63? 
72?  81?  90?"  99?  108? 

&.  What  is  l  of  18?  27?  36?  45?  54?  63?  72? 
81?  90?  99?  108? 


C.  What  part  of  9  is  1?  Of  18  is  2?  Of  27  is  3? 
Of  36  is  4?  Of  45  is  5?  Of  54  is  6?  Of  63  is  7? 
Of  72  is  8?  Of  81  is  9?  Of  90  is  10?  Of  108  is  12? 


d.  2  is  |  of  what? 
10?     11?     12? 


3?   4?  5?   6?   7?   8?   9? 


•J-  of  18  equals  what? 
•J-  of  81  equals  what? 
-^  of  63  equals  what? 
i.  of  36  equals  what? 
•£  of  72  equals  what? 


5  equals  -J-  of  what? 

7  equals  -J-  of  what? 
9  equals  J  of  what? 

11  equals  1  of  what? 

8  equals  J  of  what? 


of  9  miles?       18  rods?       27  feet?       36  inches? 


of  45  days?     54  hours?     63  minutes?     99  seconds? 
of  $72?     $  .81?     90  horses?     108  sheep? 
of  180  bushels?       270  barrels?       360  pounds? 


CHAPTER  TWO. 


85 


LESSON    XII. 


1. 

90  equals  how  many 

9's? 

11. 

56  equals  how 

many 

8's? 

2. 

45  equals  how  many 

9's? 

12. 

63  equals  how 

many 

7's? 

3. 

81  equals-  how  many 

9's? 

13. 

54  equals  how 

many 

6's? 

4. 

99  equals  how  many 

9's? 

14. 

72  equals  how 

many 

8's? 

5. 

27  equals  how  many 

9's? 

15. 

42  equals  how 

many 

7's? 

6. 

18  equals  how  many 

9's? 

16. 

72  equals  how 

many 

6's? 

7. 

86  equals  how  many 

9's? 

17. 

48  equals  how 

many 

6's? 

8. 

54  equals  how  many 

9's? 

18. 

48  equals  how 

many 

4's? 

9. 

108  equals  how  many  9's? 

19. 

48  equals  how 

many 

8's? 

10. 

63  equals  how  many 

9's? 

20. 

84  equals  how 

many 

7's? 

1. 

20  are  how  many  9 

's? 

8's? 

7's?     6's?     5' 

s?     4' 

s? 

2. 

25  are  how  many  9 

's? 

8's? 

7's?     6's?     51 

s?     4' 

s? 

3. 

83  are  how  many  9 

's? 

8's? 

7's?     6's?     5' 

s?     4' 

s? 

4. 

37  are  how  many  9 

's? 

8's? 

7's?     6's?     5' 

s?     4' 

s? 

5. 

41  are  how  many  9 

's? 

8's? 

7's?     6's?     5' 

s?     4' 

s? 

6. 

47  are  how  many  9 

's? 

8's? 

7's?     6's?     5' 

s?     4' 

s? 

7. 

52  are  how  many  9 

's? 

8's? 

7's?     6's?     51 

s?     4' 

s? 

.  8. 

63  are  how  many  9 

's? 

8's? 

7's?     6's?     5' 

s?     4' 

s? 

9. 

72  are  how  many  9 

's? 

8's? 

7's?     6's?     5' 

s?     4' 

s? 

10. 

90  are  how  many  9 

's? 

8's? 

7's?     6's?     5' 

s?     4' 

s? 

1.  If  9  yards  of  calico  cost  one  dollar,  what  part  of  a  dollar 
does  1  yard  cost  ?     2  yards  ?     3  yards  ?     4  yards  ?     5  yards  ? 
6  yards  ?     7  yards  ?     8  yards  ? 

2.  If  9  yards  of  cloth  cost  $18,  what  does  1  yard  cost?     2 
yards  ?    8  yards  ?     4  yards  ?     5  yards  ?     6  yards  ?    7  yards  ? 
8  yards  ? 


3.  What  is  1  of  $27?      f  ? 

4.  What  is  1  of  36  feet?  f? 

5.  What  is  1  of  45  cents?  |? 

6.  What  is  |  of  54?          f  ? 


!-?   I?   I? 
t? 
t? 
f? 


I? 
? 


A? 
9  ' 

"9  * 

f? 


I? 

I? 

f? 

? 


I? 

I? 
I? 


I? 
!? 


86  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XIII. 

1.  There  are  9  square  feet  in  1  square  yard.      How  many 
square  feet  in  2  square  yards?     3  square  yards? 

2.  What  will  5  dozen  eggs  cost  at  9  cents  a  dozen  ? 

3.  What  will  6  barrels  of  flour  cost  at  $9  a  barrel? 

4.  At  9  cents  a  yard,  what  will  7  yards  of  ribbon  cost  ? 

5.  What  will  8  slates  cost  at  9  cents  each  ? 

6.  How  far  can  a  man  walk  in  9  hours,  walking  9  miles  an 
hour? 

7.  When  coal  costs  $9  a  ton,  what  do  10  tons  cost? 

8.  If  9  men  can  build  a  wall  in  11  days,  how  long  will  it 
take  one  man  to  build  it  ? 

9.  If  9  men  can  do  \  of  a  piece  of  work  in  a  day,  how 
many  men  will  be  required  to  do  the  whole  of  it  ? 

10.  If  6  men  can  build  a  wall  in  12  days,  in  how  many 
days  can  9  men  build  it  ? 

11.  If  one  man  can  dig  a  ditch  in  18  days,  in-  how  many 
days  can  9  men  dig  it  ? 

12.  If  9  pounds  of  sugar  cost  54  cents,  what  is  the  price  of 
a  pound  ? 

13.  How  many  boxes  of  berries  can  be  bought  for  45  cents, 
at  9  cents  a  box  ? 

14.  At  $9  a  barrel,  how  many  barrels  of  flour  will  $63  buy? 

15.  With  90  cents,  how  many  pine-apples  can  be  bought  at 
9  cents  a  piece  ? 

16.  81  yards  of  calico  will  make  9  gowns.     How  many 
yards  will  make  one  gown  ? 

17.  $108  will  buy  9  sheep.     Price  of  one  sheep? 

18.  When  the  price  of  9  sheep  is  given,  how  do  you  find  the 
price  of  one  sheep  ? 

19.  f  45  pays  the  rent  of  a  house  one  month.    The  gas  bill  is 
•J-  of  the  rent.     What  is  paid  for  rent  and  gas  ? 

20.  If  a  year's  fuel  cost  a  family  $99  and  the  water  tax  is 
•J-  as  much,  how  many  dollars  will  be  paid  for  fuel  and  water? 


CHAPTER  TWO.  87 

LESSON     XIV. 

10  50  90 

20  60  100 

30  70  110 

40  80  120 

a.  How  many  10's  in  20?  30?  40?  50?  60?  70? 
80?  90?  100?  110?  120? 

6.  What  is  yi  of  20?  30?  40?  50?  60?  70?  80? 
90?  100?  110?  120? 

C.  2  is  ^  of  what  number?  3?  4?  5?  6?  7?  8? 
9?  10?  11?  12? 

d.   1*0  of  20  equals  what  ?     30  ?     40  ?     60  ?     100  ?     120  ? 

C.   5  is  3*0  of  what  what  number ?    4?    6?    9?     12? 

1*0  of  100  cents  ?     90  sheep  ?     70  hats  ?       30  pens  ? 
^o  of  20  dimes  ?     40  miles  ?     60  feet  ?      80  pins? 
3*5  of  120  pencils?     50  boys ?     110  girls?    150  cows? 

1.   1  cent  is  what  part  of   a  dime?     2  cents?    3  cents? 

4  cents  ?    5  cents  ?    6  cents  ?    7  cents  ?     8  cents  ?     9  cents  ? 

£.  What  part  of  1  dollar  is  1  dime  ?     2  dimes  ?    3  dimes  ? 

4  dimes  ?     5  dimes  ?     6  dimes  ?     8  dimes  ?     9  dimes  ? 

3.  There  are    10  cents  in  a  dime.     How  many  cents  in 

5  dimes  ?     10  dimes  ?     8  dimes  ?     6  dimes  ? 

4.  If  you  sleep  10  hours  each  night,  how  many  hours  do 
you  sleep  in  a  week  ? 

5.  At  10  cents  a  dozen,  what  cost  12  dozen  eggs  ? 

6.  At  10  cents  a  pound,  what  will  11  pounds  of  maple  sugar 
cost? 

7.  At  $10  a  head,  what  will  8  calves  cost? 


88  FIRST  BOOK  IAT  ARITHMETIC. 

LESSON     XV. 

11  55  09 

22  66  110 

33  .                         77  121 

44  88  132 

1.  Howmany  ll's  in  22?     55?    99?     121?     182?     99? 

2.  What  is  1^  of  44?    66?    88?     110?    77?    55?    121? 

3.  2  is  i^  of  what  number?    3?     5?     7?     9?     11?     6? 

4.  ^Y  of  99  sheep?     66  desks?     33  rods?      $121?     $88? 

5.  What  is  y1!  of  11  knives?     T2T?     ^  ?     T\     T5T?    -&  ? 

6.  What  is  -A  of  $121?    Ty    T3T?    T\    T5T?    T'r?    TV 


12  60  108 

24  72  12O 

36  84  132 

48  96  144 

1.  How  many  12's  in  24?     36?     48?     60?     72?    84? 
96?     108?     120?     132?     144? 

2.  What  is  -^  of  48?    84?    60?     120?     144?    96?    72? 

3.  2  is -^  of  what  number?    3?    4?     5?    6?    7?     8? 
9?    10?     11? 

4.  ^  of  12  inches ?     36  feet?     48  rods?     60  miles ? 

5.  Jg-  of  $108?      $132?      $144?      $96?      $72?      $96? 

6.  28  are  how  many  12's?   ll's?    10's?    7's?    9's?     8's? 

7.  37  are  how  many  12's?   ll's?    10's?    9's?     6's?     7's? 

8.  43  are  how  many  12's ?     9's?      8's?    7's?  ll's?     5's? 

9.  56  are  how  many  12's?     9's?      7's?    6's?  10's?  ll's? 
10.  67  are  how  many  12's?   ll's?      8's?    6's?    9's?     7's? 


CHAPTER  TWO.  89 

LESSON    XVI. 

1.  12  are  how  many    6's?  4's?     3's?    2's? 

2.  14  are  how  many    7's?  2's? 

3.  15  are  how  many    5's?  3's? 

4.  16  are  how  many    8's?  4's?     2's? 

5.  18  are  how  many    9's?  6's?     3's?     2's? 

6.  20  are  how  many  10's  ?  5's  ?     4's  ?     2's  ? 

7.  22  are  how  many  ll's?  2's? 

8.  24  are  how  many  12's  ?  6's  ?     4's  ?     3's  ?     2's  ? 

9.  27  are  how  many    9's  ?  3's  ? 

10.  28  are  how  many    7's  ?  4's  ? 

11.  30  are  how  many  10's  ?  6's  ?     5's  ?     3's  ? 

12.  32  are  how  many    8's  ?  4's  ? 
15.  33  are  how  many  ll's  ?  3's  ? 

14.  35  are  how  many    7's?  5's? 

15.  86  are  how  many  12's  ?  9's  ?     6's  ?     4's  ? 
70.  40  are  how  many  10's ?  8's  ?     6's ?     4's? 

1 7.  42  are  how  many    7's?  6's? 

18.  44  are  how  many  ll's  ?  4's  ? 

10.  45  are  how  many    9's?  5's?    8's? 

20.  48  are  how  many  12's  ?  8's  ?     6's  ?     4's  ? 

5.Z.  50  are  how  many  10's  ?  5's  ? 

£2.  54  are  how  many    9's?  6's? 

23.  55  are  how  many  ll's  ?  5's  ? 

54.  56  are  how  many    8's?  7's? 

25.  60  are  how  many  12's  ?  10's  ?     6's  ?     6's  ? 

££.  63  are  how  many    9'o?  7's? 

£7.  66  are  how  many  ll's  ?  6's  ? 

58.  70  are  how  many  10's?  7's? 

29.  72  are  how  many  12's  ?  9's  ?     8's  ?     6's  ? 

50.  77  are  how  many  ll's?  7's? 

31.  80  are  how  many  10's  ?  8's  ? 

55.  84  are  how  many  12's  ?  7's  ? 


90  FIRST  BOOK  IN  ARITHMETIC. 

LESSON     XVII. 
MEASURES    OF    LENGTH. 


ONE  INCH.  TWO  INCHES. 

THREE  INCHES. 

We  measure  lines  to  find  their  length.  Lines  are  measured 
by  means  of  other  lines  of  known  length.  A  foot  is  the  name 
of  a  line  of  known  length.  The  other  lines  of  known  length 
are  the  mile,  the  rod,  the  yard,  and  the  inch. 

A  Table  shows  the  relation  of  these  lines  to  each  other. 

12  inches=l  foot.  1  mile— 320  rods.  1  inch=T^  of  a  foot. 

3  feet=l  yard.  1  rod =16^  feet.  1  foot= J-  of  a  yard. 

5£  yards =1  rod.  1  rod=:5^  yards.  1  yard— T2T  of  a  rod. 

16£  feet=l  rod.  1  yard=3  feet.  1  Tod^yJ-g-of  amile. 

320  rods=l  mile.  1  foot =12  inches. 

1.  How  long  is  your  slate?     Draw  a  line  on  the  black- 
board as  long.    How  wide  ?   Draw.    How  long  is  your  Eeader  ? 
Draw.     How  long  is  a  pane  of  glass  in  your  school  room  ? 
How  wide  ?    Draw  lines  3  in<5hes,  4  inches,  6  inches,  9  inches, 
12  inches,  15  inches,  18  inches,  24  inches  in  length. 

2.  How  long  is  your  desk  ?    How  wide  ?    How  long  is  the 
teacher's  table?    How  wide?    How  long  is  the  teacher's  plat- 
form ?     How  wide  ?     How  long  are  the  music  lines  in  your 
room  ?     What  is  the  height  of  the  windows  ?     Of  the  doors  ? 
Of  your  room  ? 

3.  What  is  the  length  of  a  block  in  Chicago,  as  from  Madi- 
son to  Washington  streets  ?    How  far  is  it  from  the  City  Hall 
to  the  Custom  House  ?    How  far  is  it  from  Madison  street  to 
Twelfth  street  ?    From  State  street  to  Halsted  ?    From  Mad- 
ison street  to  Chicago  avenue  ? 


CHAPTER  TWO.  91 

LESSON     VIII. 

1.  How  many  inches  in  2  feet?     3  feet?     4  feet?     5  feet? 
6  feet?     7  feet?     8  feet?     9  feet?     10  feet?     11  feet?     12 
feet? 

2.  How  many  feet  in  4  yards?     6  yards?     9  yards?     11 
yards  ?     20  yards  ? 

3.  How  many  feet  in  36  inches  ?     60  inches  ?     48  inches  ? 
72  inches  ?     96  inches  ? 

4.  11  yards = how  many  rods? 

5.  What  part  of  a  mije  is  160  rods?     80  rods?     40  rods? 

6.  How  many  inches  are  2  feet  10  inches  ?    3  feet  6  inches  ? 
4  feet  4  inches  ?     1  foot  11  inches  ? 

7.  How  many  rods  in  2  miles  ? 
<5.  How  many  feet  in  a  mile? 

P.  How  many  inches  in  a  yard?     2  yards? 

10.  How  many  inches  in  £  of  a  yard? 

11.  How  many  inches  in  £  of  a  yard? 

12.  How  many  inches  in  \  of  a  yard? 

15.  How  many  inches  in  \  of  a  yard? 

14.  One-eighth  of   a  mile  is  sometimes  called  a  furlong. 
How  many  furlongs  make  a  mile? 
Ic5.  How  many  rods  in  a  furlong? 

16.  How  many  rods  in  £  of  a  furlong? 

17.  How  many  rods  are  £  plus  J  of  a  furlong? 

18.  A.  line  6  feet  long  is  sometimes  called  a  fathom.     It  is 
used  in  measuring  the  depth  of  the  ocean.     What  does  "  Full 
forty  fathoms  down"  mean? 

19.  How  many  yards  in  a  fathom  ? 

20.  How  many  feet  in  5  yards  2  feet? 

21.  At  $£  a  foot  what  will  6  yards  2  feet  of  lead,  pipe  cost? 

22.  How  far  is  it  from  the  City  Hall  to  Western  avenue? 

23.  How  far  is  it  from  the  City  Hall  to  Fullerton  avenue? 

24.  How  far  is  it  from  the  City  Hall  to  Thirty-ninth  street  ? 


92  FIRST  BOOK  IN  ARITHMETIC. 

LESSON     XIX. 
MEASURES    OF    WEIGHT. 


Tea,  coffee,  sugar,  flour  and  coal  are  measured  by  weight; 
coal  by  the  ton;  flour  by  the  hundred-weight  (cwt.),  i.  e.,  one 
hundred  pounds;  tea  and  coffee  by  the  pound  (R>.) ;  and  spices 
by  the  ounce  (oz.). 

TABLE. 

16  ounces  (oz.)=:l  pound  (R>.) 
100  pounds      =1  hundred- weight  (cwt.). 
2000  pounds     =1  ton  (T.). 
T.  =  20   cwt.  — 2000  Ibs.  =  32000  oz. 

1.  How  many  ounces  are  there  in  2  Ib.  ?     3  Ib.  ?     4  Ib.  ? 
5  ft.?     2R).  2oz.?     3  ft.  2oz.?     4  Ib.  4  oz.  ?     5  Ib.  5oz.? 

2.  How  many  pounds  in  5  cwt.  ?     1  cwt.  ?     9  cwt.  ? 
5.  J  of  a  ton = how  many  pounds? 

4.  500  pounds  is  what  part  of  a  ton? 

5.  1  oz.  is  what  part  of  a  pound?     2  oz.  ?     3  oz.  ?     4  oz.  ? 
5  oz.  ? 

6.  How  many  boys,  weighing  100  Ibs.  each,  would  weigh  a 
ton? 

7.  What  weights  would  a  grocer  use  in  weighing  24  ounces 
of  pepper? 

8.  How  many   4  oz.  weights  exactly  balance   the   1   Ib. 
weight  ? 

9.  How  many  2  oz.  weights  make  a  pound  ? 

10.  How  many  1  Ib.  weights  would  balance  four  8  oz.  and 
four  4  oz.  weights? 


CHAPTER  TWO. 


LESSON    XX. 

MEASURES    FOR    GRAINS,    SEEDS,  ETC. 


93 
*     «" 


Corn,  wheat,  and  potatoes  are  measured  by  the  bushel.    Peas 
and  beans  are  sold  by  the  peck,  half  peck,  and  quart. 


TABLE. 


2  pints  (pt.)  =  l  quart  (qt.). 
8  quarts  =1  peck  (pk.). 
4  pecks  =1  bushel  (bu.) 


1  bu=4  pks. 
1  pk=8  qts. 
1  qt=2  pts. 


1  bu.  =  4  pks.  =  32  qts. =64  pts. 

1.  How  many  pints  in  8  qts.  ?    12  qts.  ?    25  qts.  ?    50  qts.  ? 

2.  How  many  quarts  in  5  pks.  ?    7  pks.  ?    9  pks  ?    12  pks.  ? 

3.  How  many  pecks  in  8  bu.  ?     9  bu.  ?     12  bu.  ?     28  bu.  ? 

4.  How  many  quarts  in  20  pts.  ?     30  pts.  ?     40  pts.  ?     50 
pts.  ?     60  pts.  ?     90  pts.  ? 

5.  How  many  pecks  in  24  qts.  ?    48  qts.  ?    72  qts.  ?  96  qts.  ? 

6.  How  many  bu.  in  8  half  bushels  ?     48  pks.  ?     2  half  bu. 
and  8  pks.  ?     5  half  bu.  and  2  pks.  ? 

7.  What  part  of  a  pk.  is  1  qt.  ?     3  qts.  ?     5  qts.  ?     7  qts.  ? 
(9.  What  part  of  a  bu.  is  1  pk,  ?     2  pecks.  ?     a  half  bu. 

and  a  pk.  ? 

9.  How  many  qts.  in  1  half  bu.  and  3  pks.  ?     5  pks.  and 
3  qts.  ?     1  bu.  and  1  pk.  ? 

10.  Cost  of  a  pk.  of  potatoes  at  60  cents  a  bu.  ? 

11.  Cost  of  a  qt.  of  beans  at  64  cents  a  peck? 


94  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XXL 

MEASURES    FOR    OIL   AND    MILK. 


The  measures  used  by  the  grocer  in  measuring  vegetables 
and  fruit  are  made  of  wood.  For  measuring  oil  and  milk,  tin 
measures  are  used.  These  tin  measures  are  the  gallon,  half- 
gallon,  quart  and  pint. 

TABLE. 

2  pints    —  1  quart. 
4  quarts  =  1  gallon     (gal). 
1  gallon =4  quarts— 8  pints. 

1.  How  many  quarts  can  be  drawn  from  a  10  gallon  can  of 
oil? 

2.  Cost  of  6  quarts  of  oil  at  4  cents  a  quart  ? 

3.  How  many  pints  in  2  gallons  and  3  quarts'? 
4. .  3  quarts  is  what  part  of  2  gallons  ? 

5.  With  milk  at  24  cents  a  gallon,  how  many  pint  milk 
tickets  can  be  bought  for  48  cents  ? 

6.  With  milk  at  25  cents  a  gallon,  how  many  quart  tickets 
can  be  bought  for  $1? 

7.  How  does  the  grocer  measure  a  quart  of  beans?    A 
quart  of  oil  ? 

8.  96  pints  of  beer  are  how  many  gallons?     96  pints  of 
beans  are  how  many  half  pecks  ? 

9.  How  many  pint  cupfuls  of  water  will  fill  a  10  gallon  pail  ? 

10.  From  a  gallon  can  of  oil,  3  pints  were  spilled.     How 
many  pints  remained  ? 


CHAPTER  TWO.  95 

LESSON    XXII. 

U.  S.    MONEY. 

Money  is  the  measure  of  value.  What  is  the  book  worth  ? 
It  is  worth  One  Dollar.  $1.  measures  the  value  of  the  book. 
The  units  of  value  are :  one  dollar,  one  dime,  one  cent,  one  mill. 

TABLE. 

10  mills   =  1  cent. 

10  cents   =  1  dime. 

10  dimes  =  1  dollar. 

$1.  =  10  dimes  =  100  cents  =  1000  mills. 

In  reading  figures  used  to  represent  money  values  the  dime 
unit  is  not  used.  8  dimes  is  read  80  cents.  2  dimes  and  5 
cents  is  read  25  cents. 

In  writing  dollars,  cents  and  mills,  the  dollar  sign  ($)  and 
the  period  ( . ),  called  the  decimal  point,  must  always  be  used. 
The  sign  $  is  placed  before  or  at  the  left  of  the  number  and 
the  decimal  point  between  dollars  and  cents,  or  at  the  left  of 
cents. 

For  5  dollars  write  $5. 

For  50  cents  write  $  .50. 

For  5  cents  write     $  .05. 

For  5  mills  write     $  .005. 

For  250  cents  write  $2.50. 

Read:         $     6.85  $800.08  $         .995 

$  31.095  $     9.09  $       9.999 

$     5.50  $       .25  $         .184 

$210.10  $       .758  $1000.10 

$201.015  $       .005  $2500.25 

$  20.20  $       .125  $5090. 


96 


FIRST  BOOK  IN  ARITHMETIC. 


LESSON     XXIII. 

Write:     Two  dollars,  twenty-three  cents,  five  mills. 

3  dollars,  3  cents,  3  mills. 

One  hundred  eighteen  dollars  and  twenty-five  cents. 

605  dollars  and  nine  cents. 

2  thousand  dollars  and  8  mills. 

200  ninety  dollars  fourteen  cents. 

Twenty-five  dollars  and  twenty-five  cents. 

Seventy-five  cents. 

Seven  cents  and  5  mills. 

300  cents. 


1.  Add  $1.25 

$    .75 


2.  From  $20.50 
Take  $19.60 


8.  $   .09x9= 

$  .90x9= 
$9.  x9= 
$9.09x9= 
$2.75x8= 

4.  I  of  $54.54? 


$1.18 

$20.25 

$1,185 

$   .68 

$20.75 

$3,715 

$40.25 

$10.75 

$16. 

$10.50 

$  5.80 

$  8.50 

$    .10x10= 

$   .12x12  = 

$    .20x10= 

$1.50x10= 

$1.60x    5= 

5.  |  of  $49.63? 


$18.24? 
$6.30? 


$42.48? 
$8.40? 


6.  What  would  2  dozen  Headers  cost  at  $.90  each? 

7.  What  would  8  horses  cost  at  $125  each? 

8.  If  9  acres  of  land  cost  $360,  what  would  8  acres  cost  ? 

9.  If  8  cords  of  wood  are  worth  $32,  what  are  $24  cords 
worth  ?     36  cords  ? 

10.  What  will  45  pounds  of  beef  cost  if  8  pounds  cost  $.96  ? 


CHAPTER  TWO,  97 

LESSON    XXIV. 

NOTATION  AND  NUMERATION. 

In  language,  number  is  expressed  by  words,  answering  the 
question  "How  many?" 

The  snow-plow  was  drawn  by  eight  horses.  How  many 
horses  ?  Eight, 

Expressions  of  quantity  answer  the  question,  "How  much?" 
As :  A  ton  of  coal ;  a  barrel  of  sugar. 

In  arithmetic,  number  is  represented  by  figures.  There  are 
ten  characters  or  figures  used. 

The  expressing  and  reading  of  numbers  by  means  of  these 
ten  characters  is  called  Notation  and  Numeration, 

The  figures :  1,  2,  3,  4,  5,  6,  7,  8,  9,  represent  some- 
thing of  number  or  quantity . 

The  tenth  character  0,  zero  or  naught  (sometimes  called  a 
cipher),  represents  nothing  of  number  or  quantity. 

In  writing  numbers,  the  nine  figures  are  used  to  express 
ones,  tens,  hundreds,  thousands,  ten-thousands,  hundred- 
thousands,  millions,  etc.,  as  is  shown  in  the  following  columns, 
arranged  thus : 

Ten-  Hundred- 

Ones.  Tens.       H'ds.         Thous.        Thousands.      Thousands.  Millions. 

1.  10.  100.  1  000.  10  000.  100  000.  1  000  000. 

2.  20.  200.  2  000.  20  000.  200  000.  2  000  000. 

3.  40.  300.  3  000.  30  000.  800  000.  3  000  000. 

4.  40.  400.  4  000.  40  000,  400  000.  4  000  000. 

5.  50.  500.  5  000.  50  000.  500  000.  5  000  000. 

6.  60.  600.  6  000.  60  000.  600  000.  6  000  000. 

7.  70.  700.  7  000.  70  000.  700  000.  7  000  000. 

8.  80.  800.  8  000.  80  000.  800  000.  8  000  000. 

9.  90.  900.  9000.  90000.  900000.  9000000. 


98  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XXV. 

11  (eleven)  is  10  and  1.     One  ten  and  one. 

13  (thirteen)  is  10  and  3.     One  ten  and  three. 

34  (thirty-four)  is  30  and  4.     Three  tens  and  four. 

58  (fifty-eight)  is  50  and  8.     Five  tens  and  eight. 

125  (one  hundred,  twenty-five)  is  100,  20  and  5.  One 
hundred,  two  tens,  and  five. 

8456  (three  thousand,  four  hundred,  fifty-six),  is  3000,  400, 
50,  and  six. 

Express  the  following  in  figures  : 
One  hundred,  two  tens,  and  five. 
Four  hundreds,  five  tens. 
Seven  hundreds,  five  tens  and  six. 
Eight  hundreds,  nine  tens  and  one. 
Three  hundreds,  nine  tens  and  one. 
Five  hundreds,  three  tens  and  seven. 
Nine  hundreds,  nine  tens  and  nine. 
Six  hundreds,  six  tens  and  six. 
Two  hundreds,  three  tens  and  one. 
Eleven  hundreds,  one  ten  and  one. 
Thirteen  hundreds,  three  tens  and  three. 

Two  hundred.  Nine  hundred. 

Two  hundred,  forty.  Nine  hundred,  forty. 

Eight  hundred,  five.  Six  hundred,  seventy. 

Three  hundred,  fifty.  Five  hundred,  eighty. 

Three  hundred,  forty.  Five  hundred,  twenty. 

Five  hundred,  ninety.  Seven  hundred,  thirty. 

One  hundred,  ten.  Six  hundred,  ten. 

When  three  figures  are  written  side  by  side,  what  does  the 
one  at  the  right  represent  ?  The  one  next  to  it  ?  The  one  at 
the  left? 


CHAPTER  TWO.  99 

LESSON     XXVI. 

Write  in  figures : 

7.  Eight  thousand  seven  hundred  three,  four  thousand  forty- 
five,  six  thousand  three  hundred  eight,  forty-eight 
hundred. 

2.  Five  thousand  forty-eight,  nineteen  hundred  ninety,  seven 

thousand  eighty-two,  eight  thousand  fifty. 

3.  Seven  thousand   two  hundred  forty,  nine  thousand  nine 

hundred  nineteen,  six  thousand  seven,  eight  thousand 
seven  hundred  seventy  -six. 

4.  Seven  thousand   one  hundred  seven,   six  thousand  eight 

hundred   four,   nine    thousand   one   hundred  ten,  five 
thousand  five  hundred  fifty. 

5.  Six  thousand  eighty-six,  four  thousand  forty,  one  thousand 

ten,  nine  thousand  ninety-nine. 

6.  Eight   thousand   eighty,   seventeen    hundred    fifty-seven, 

eleven  hundred  one,  seven  thousand  seven. 

Head  the  following : 

1.  100  000  9  400  469  346 
250  118                       90  009                     868  569 

19  019  900  090  211  Oil 

468  910  654  480  404  404 

2.  In  the  number  384  578,  what  do  the  three  figures  at  the 
right  represent  ?    Am.  Units,  tens,  hundreds. 

3.  What  do  the  three  figures  at  the  left  represent  ? 

Ans.  Units,  tens,  hundreds  of  thousands. 

4.  A  Period  is  a  group  of  three  figures  representing  units, 
tens,  hundreds,  of  any  denomination. 

5.  How  many  periods  in  the  number  500  000  ? 

6.  What  is  the  denomination  of  the  first  or  right  hand 
period  ? 

7.  What  is  the  name  of  the  second  period  ? 


100  FIRST  BOOK  IN  ARITHMETIC. 

8.  Bead :  100  000  000.  40  060  018. 

120  240  300.  5  009  005. 

468  519  181.  15015  015. 

116  116  116.  160116  161. 

875  498765.  1001  001. 

9.  In  the  number  342  416  518,  how  many  periods? 

10.  What  is  the  denomination  of  the  third  period  ? 

11.  What  do  the  figures  of  the  left  hand  period  represent  ? 


LESSON    XXVII. 

ADDITION. 

6,  4  and  10  are  how  many  ? 

This  is  called  a  question  in  Addition.     We  put  together,  or 
add,  6,  4  and  10  to  find  their  sum  or  amount. 
The  sum  of  6,  4  and  10  is  20. 

Find  the  sum  of : 


1. 

6 

6 

6 

6 

6 

6 

6 

6 

6 

4 

6 

6 

6 

6 

6 

6 

5 

4 

5 

4 

6 

6 

6 

6 

6 

6 

6 

6 

4 

3 

6 

6 

6 

6 

6 

5 

4 

5 

8 

5 

6 

6 

6 

6 

6 

4 

6 

6 

2 

6 

1 

2 

3 

4 

5 

3 

3 

2 

6 

6 

2. 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

6 

7 

7 

7 

7 

7 

7 

7 

7 

5 

5 

7 

7 

7 

7 

7 

7 

7 

4 

4 

4 

7 

7 

7 

7 

7 

7 

6 

6 

6 

3 

7 

7 

7 

7 

7 

8 

5 

3 

3 

2 

1 

2 

3 

4 

5 

6 

4 

2 

4 

7 

CHAPTER  TWO.  101 


LESSON    XXVIII. 

Add  the  columns  in  this  Lesson  from  the  bottom  up,  from 
the  top  down,  from  right  to  left,  from  left  to  right. 


1.    8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

7 

2 

8 

8 

8 

8 

8 

8 

8 

8 

6 

6 

8 

8 

8 

8 

8 

8 

8 

8 

8 

4 

8 

8 

8 

8 

8 

8 

8 

7 

5 

7 

8 

8 

8 

8 

3 

8 

8 

6 

4 

3 

8 

8 

8 

8 

8 

8 

8 

5 

8 

5 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

1 

2 

3 

4 

5 

6 

7 

4 

3 

5 

2.    9 

9 

9 

9 

9 

9 

1 

9 

9 

9 

9 

9 

9 

6 

9 

8 

3 

5 

9 

9 

9 

9 

8 

5 

9 

7 

2 

6 

9 

9 

9 

9 

8 

9 

7 

6 

4 

8 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

8 

7 

8 

7 

5 

6 

2 

7 

9 

6 

8 

8 

5 

7 

4 

8 

3 

9 

9 

7 

8 

5 

5 

9 

9 

9 

6 

9 

9 

5 

8 

6 

5 

2 

3 

9 

7 

1 

2 

3.     8 

8 

9 

6 

8 

3 

7 

5 

4 

8 

5 

7 

3 

6 

8 

3 

8 

8 

5 

3 

7 

5 

7 

6 

4 

5 

9 

7 

2 

9 

6 

6 

6 

5 

4 

5 

6 

8 

2 

2 

3 

4 

5 

5 

7 

7 

5 

2 

7 

7 

3 

2 

2 

5 

8 

7 

4 

9 

3 

4 

7 

8 

8 

7 

9 

9 

2 

3 

6 

6 

8 

9 

6 

7 

7 

9 

7 

8 

5 

5 

4 

3 

4 

8 

6 

6 

9 

4 

4 

4 

9 

7 

9 

2 

6 

4 

1 

4 

5 

7 

102  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XXIX. 

Facts  to  be  memorized. 

How  many  are : 

6  and  6?  6  and  10?  8    5    7    9    4 

6  and  5  ?  6  and  9  ?          _6    6    6    6    6 

6  and  7  ?  6  and  8  ? 

7  and  7?  7  and  10?  5    4    6    9    8 
7  and  6  ?  7  and  9  ?         __7  __7    7   J7    7 

7  and  8  ?  7  and  5  ? 

8  and  8  ?  8  and  6  ?  4    6    5    7    9 

8  and  7  ?  8  and  5  ?         _8  _8  _8  __8   _$ 

9  and  9?  9  and  7?  5    7    4    6    8 
9  and  8?  9  and  6?         __9  _9  _9  __9  __9 

Suggestion: 

6-f7  =  6+4+3  =  10+3  =  13. 
7+8  ==  7+3+5  =  10+5  =  15. 
8+9  =±  8+2+7  =  10+7  =  17. 

The  grouping  and  adding  of  numbers  by  tens  will  help  to 
secure  accuracy  and  rapidity.  Both  accuracy  and  rapidity  in 
adding  must  be  secured  to  the  child  or  the  work  of  the  teacher  is  a 
failure. 


Find 

the  sum: 

1. 

7 

17 

27 

47 

97 

77 

57 

37 

87 

68 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

2. 

8 

18 

38 

58 

78 

98 

68 

48 

88 

28 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

3. 

9 

19 

29 

49 

59 

79 

99 

39 

69 

89 

6 

6 

6 

6 

6 

6 

5 

6 

6 

6 

CHAPTER  TWO.  103 

LESSON    XXX. 


1. 

8 

18 

38 

58 

98 

78 

48 

68 

88 

28 

2. 

9 

29 

49 

69 

89 

99 

59 

79 

39 

109 

3. 

9 

49 

29 

59 

39 

69 

89 

79 

99 

109 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

4. 

14 

25 

36 

47 

58 

69 

75 

84 

98 

77 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

5. 

13 

24 

35 

56 

47 

88 

79 

87 

95 

99 

1.  What  is  the  sum  of  $203,  $176  and  $510? 

2.  What  is  the  sum  of  124  bu.,  403  bu.,  and  271  bu.  ? 

3.  What  is  the  sum  of  785  tons,  948  tons,  and  370  tons  ? 

4.  What  is  the  sum  of  267  rods,  565  rods,  and  97  rods  ? 

5.  What  is  the  sum  of  342  feet,  706  feet,  and  680  feet? 

Arrange  in  columns  and  add: 

6.  $11.36,  $26.07,  $9.16,  $32.76,  and  $2.34. 

7.  $42.06,  $10.30,  $4.82,  $.77,  and  $.93. 

8.  $370.21,  $2.49,  $3.07,  and  $94. 

9.  $32.50,  $126.08,  $9.40,  $15.74,  and  $140. 

10.  $307.09,  $50,  $6.84,  $100.10,  and  $450. 

11.  $76,  $400,  $5.12,  $17.04,  f  .97,  and  $1.62. 


104 


FIRST  BOOK  IN  ARITHMETIC. 


LESSON    XXXL 

1.  Add  together  39,  67,  92,  43,  84,  61. 

2.  Add  together  270,  489,  126,  46. 

3.  Add  together  2368,  235,  496,  1736. 

4.  Add  together  66,  476,  801,  4009,  32,  127. 

Add: 


5. 

12345 

6.  23456 

7.     5 

8.  92583 

3275 

72564 

23 

4620 

4721 

3785 

936 

973 

371 

23584 

6543 

25 

51028 

987 

92840 

9 

61234 

96 

72104 

17 

9. 

23504 

10.   358 

11.  56789 

12.  123456 

4368 

9246 

3587 

258071 

25 

14376 

296 

589347 

9 

845 

89 

258923 

36 

29 

7 

720145 

378 

7 

12345 

396012 

1.  124+445-{,308+568+678+244+458+27+9+27. 

2.  275+808+42+606+8+640+816+46+22+582. 

3.  675+342+460+465+25+378+4,232+3645+8. 

4.  2465+478+3+495+756+4386+760+28+717. 

5.  371+24+684+6543+845+78+36+1234. 

6.  868+868+796+677+908+809+117. 

7.  1051+2482+6384+5768+4648+3456. 

8.  5129+36428+420564+43476+590+864. 

9.  490+590+690+790+890+990+1090. 
10.  2500+3600+4700+5800+6900+8+8+8. 


CHAPTER  TWO. 


105 


LESSON    XXXII. 

SUGGESTION:    In  adding  long  columns  of  figures  some  test  of 
accuracy  is  desirable.     Make  three  additions  thus: 


678456 

3  6 

486645 

4  7 

5  5 

879586 

4  1 

4  6 

685497 

3  9 

3  9 

789987 

4  6 

4  1 

194538 

5  5 

4  7 

485648 

3  6 

4200357 

Begin  at  the  top  of  the 
left  hand  column  and  add 
down.  Place  the  sum  of 
column  to  the  left,  as 
above. 


4200357 


Examples  for  practice. 

1.  68015          2. 

72408 

46768  • 

80803 

87385 

87586 

85408 

56828 

98586 

83584 

74358 

57326 

48816 

78587 

4.  9219          5. 

17908 

6980 

92895 

7096 

77589 

9359 

75991 

8987 

11809 

7899 

99793 

7908 

78080 

4200357 

Begin  at  the  bottom  of 
the  right  hand  column  and 
add  up.  Place  the  sum  of 
each  column  to  the  right, 
as  above. 


3.  878583 
850728 
747816 
568351 
685820 
738218 
987800 

6.  729509 
896895 
921959 
793297 
879656 
690099 
986905 


106  FIRST  BOOK  IN  ARITHMETIC. 

LESSON     -XXXIII. 

1.  A  farmer  sold  a  cow  for  22  dollars,  a  ton  of  hay  for  11 
dollars,  and  a  calf  for  7  dollars;  what  did  he  receive  for  all? 

2.  A  traveler  walked  30  miles  one  day,  26  miles  the  next, 
and  21  miles  the  next;    how  many  miles  did  he  travel  in  the 
three  days? 

3.  One  day  Sarah  wrote  in  her  copy-book  18  lines,  Maria 
16,  and  Carrie  15;  how  many  lines  did  they  all  write? 

4.  A  man  gave  60  dollars  for  a  horse,  23  dollars  for  a  saddle, 
and  9  dollars  for  a  bridle;   what  was  the  cost  of  the  whole? 

5.  A  boy  received  36  cents  on  his  birthday,  34  cents  on 
Christmas  day,  and  27  cents  on  New- Year's  day;    how  many 
cents  did  he  receive? 

6.  A  man  bought  a  piece  of  land  for  56  dollars,  and  paid  25 
dollars  for  fencing  it;  for  how  much  must  he  sell  ifc  to  gain  15 
dollars? 

7.  In  an  orchard  there  were  found  12  apples  under  one 
tree,   15  under  another,    11    under    another,    and   9  under 
another;    how  many  apples  under  the  four  trees? 

8.  A  grocer  bought  some  hams  for  20  dollars,  some  oats  for 
19  dollars,  some  fowls  for  16  dollars,   and  five  barrels  of  ap- 
ples for  10  dollars;  what  did  he  pay  for  all? 

9.  A  miller  shipped  by  railroad  28  barrels  of  flour  at  one 
time,  37  at  another,  and  40  at  another;  how  many  barrels 
did  he  ship? 

10.  If  for  paper  you  pay  45  cents,  for  envelopes  15  cents, 
stamps  12  cents,  pens  8  cents;  how  many  cents  do  you  pay 
for  your  stationery? 

11.  A  drover  bought  26  sheep  of  one  man,  30  of  another, 
37  of  another,  and  40  of  another;  how  many  sheep  did  he 
purchase? 

12.  Bought  a  horse  for  75  dollars,  and  sold  him  so  as  to 
gain  25  dollars;  how  much  did  I  receive  for  him? 


CHAPTER  TWO.  107 

LESSON    XXXIV. 

1.  A  lady  went  shopping,  and  bought  a  silk  dress  for  22 
dollars,  a  muff  for  16  dollars,  a  shawl  for  14  dollars,  and  had 
7  dollars  left;  how  much  money  had  she  at  first? 

2.  Peter  bought  a  knife  for  35  cents ;    he  gave  the  knife 
and  12  cents  for  a  sled,  which  he  sold  so  as  to  gain  10  cents 
on  the  cost;  how  much  did  he  receive  for  the  sled? 

3.  In  a  certain  orchard  are  31  apple  trees,  27  "peach  trees, 
and  19  pear  trees;  how  many  trees  in  the  orchard? 

4.  A  farmer  raised  54  bushels  of  wheat,  66  bushels  of  oats, 
and  40  bushels  of  corn;  how  many  bushels  of  grain  did  he 
raise  ? 

5.  If  it  be  62  feet  from  the  ground  to  the  belfry  of  a  church, 
and  76  feet  from  the  belfry  to  the  top  of  the  steeple,  how  high 
is  the  top  of  the  steeple  from  the  ground? 

6.  In  March  are  31  days,  in  April  30,  in  May  31 ;  how  many 
days  in  those  three  months  ? 

7.  If  a  farm  contain  83  acres  of  cleared  land  and  25  acres 
of  wood  land,  how  many  acres  are  in  the  whole  farm? 

8.  The  distance  from  Boston  to  Worcester  is  44  miles,  from 
Worcester  to  Warren  29  miles,  and  from  Warren  to  Spring- 
field 25  miles;  how  many  miles  from  Boston  to  Springfield? 

9.  Batavia  is  37  miles  west  from  Eochester,  and  31  miles 
east  from  Buffalo  by  railroad ;  what  is  the  distance  from  Eoch- 
ester to  Buffalo? 

10.  A  tailor  bought  three  pieces  of  cloth,  the  first  contain- 
ing 29  yards,   the  second  26  yards,  and  the  third  25  yards; 
how  many  yards  did  the  three  pieces  contain? 

11.  A  carriage-maker  sold  a  carriage  for  15  dollars,  and  a 
sleigh  for  48  dollars;  what  did  he  receive  for  both? 


108  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XXXV. 

1.  A  lady  bought  a  carriage  for  $275,  a  horse  for  $216,  and 
a  harness  for  $49;  how  much  did  she  pay  for  all? 

2.  A  grocer  bought  3  hogsheads  of  sugar,  containing  1467 
lb.,  1324  lb.,  and  1296  Ib. ;  also  two  barrels  containing  254 
lb.,  and  237  lb. ;  how  much  did  he  buy? 

3.  Mr.  Smith's  house  and  lot  cost  him  $7290;  for  how 
much  must  he  sell  them  to  gain  $1896? 

4.  There  are  576  sheep  in  one  flock,   753  in  another,  and 
598  in  a  third;  how  many  in  the  three  flocks? 

5.  In  one  school  there  are  298  boys  and  319  girls,  in  an- 
other 786  boys  and  739  girls,  in  a  third  917  boys  and  986 
girls;    how  many  boys  in  the  three  schools?      How  many 
pupils? 

6.  A  merchant's   sales  were   $179  on  Monday,  $215  on 
Tuesday,  $207  on  Wednesday,  $173  on  Thursday,   $198  on 
Friday,  and  $239  on  Saturday;  what  was  the  amount  of  his 
sales  for  the  week? 

7.  In  one  town  there  are  7889  people,  in  another  12873,  in 
a  third  14796,  in  a  fourth  10098,  in  a  fifth  9886;  how  many 
people  in  the  five  towns? 

8.  A  is  worth    $7859,   B  is   worth  $19868,  C  is  worth 
$9796,  D  is  worth  $29560,  E  is  worth  $19840;    how  much 
are  they  all  worth? 

9.  A  dealer  sold  six  loads  of  coal,  weighing  2978  lb.,  8144 
lb.,  2706  lb.,  2198  lb.,   2896  lb.,  and  3273  lb.;    how  many 
pounds  did  the  six  loads  weigh  ? 

10.  A  man  bought  a  lot  of  land  for  $7960,  built  a  house 
on  it  costing  $4719,  added  other  improvements  worth  $4090, 
and  sold  the  whole  at  a  gain  of  $2750;  how  much  did  he  get 
for  the  property? 

11.  A  man  born  in  1819,  died  when  he  was  57  years  old; 
in  what  year  did  he  die? 


CHAPTER  TWO.  109 

LESSON    XXXVI. 

1.  A  man  traveled  250  miles  by  railroad,  325  by  steam- 
boat, and  190  by  stage.     How  many  miles  did  he  travel? 

2.  Three  persons  deposited  money  in  a  bank.     The  first 
put  in  192  dollars,  the  second  466  dollars,  and  the  third  825 
dollars.     How  much  money  did  they  deposit? 

3.  A  man  paid  out  $5719  and  had  $8956  left;  how  much 
had  he  at  first? 

4.  The  population  of    six  towns  is:     5860,    8748,    8087, 
3746,  4875,  5390.     Find  the  whole  population. 

5.  A  house-lot  cost  $875.     For  building  a  house  there  was 
paid  to  carpenters,   $2487;   to  masons,   $680;   to  painters, 
$339.     What  was  the  entire  cost  of  house  and  lot? 

6.  A  collector  collected  on  Monday  $817.75;  on  Tuesday, 
$947.50;  on  Wednesday,  $170.90;  on  Thursday,  $5687.48; 
on  Friday,  $275.42.     Saturday  was  a  holiday.     What  did  the 
week's  collections  amount  to  ? 

7.  Bought  a  sleigh  for  $175,  a  carriage  for  $375,  pair  of 
horses  for  $480,  and  a  set  of  harness  for  $150.      Find  entire 
cost. 

8.  Six  loads  of  flour  weighed  as  follows:     3560  pounds, 
4980  pounds,  3760  pounds,  4,768  pounds,  3490  pounds,  4376 
pounds.     What  was  the  weight  of  the  six  loads  ? 

9.  A  man  paid  $8090  for  656  horses,  $7880  for  842  horses, 
and  $9988  for  758  horses.     How  many  horses  did  he  buy  and 
what  did  they  cost  him  ? 

10.  How  many  bricks  are  6666  bricks,  7777  bricks,  8888 
bricks,  and  9999  bricks? 


110  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XXXVII. 

SUBTRACTION. 

1.  If  from  a  dish,  containing  15  eggs,  7  eggs  be  taken,  what 
number  of  eggs  will  remain  in  the  dish  ? 

This  is  a  question  of  Subtraction. 
You  have  learned  that  7  and  8  are  15. 
Therefore,  15  less  7  equals  8. 

2.  The  operation  of  taking  a  part  out  of  a  whole  to  see  what 
is  left  is  Subtraction. 

3.  The  whole  number  (15  eggs)  is  called  the  Minuend* 

4.  The  part  taken  (7  eggs)  is  called  the  Subtrahend. 

5.  The  part  left  or  remaining  (8  eggs)  is  called  the  Dif- 
ference or  Remainder. 

6.  The  Minuend  is  the  whole,  of  which  the  Subtra- 
hend and  Difference  are  the  parts. 

7.  To  find  what  number  added  to  the  Subtrahend  will 
equal  the  Minuend  is  the  problem  of  Subtraction. 

8.  Minuend  =  subtrahend  -+-  difference. 
Minuend  —  subtrahend  =  difference. 
Minuend  —  difference  =  subtrahend. 

9.  If  out  of  the  sum  of  $25,  $17  be  paid,  how  many  dol- 
lars remain  ? 

What  is  the  minuend  ? 

What  is  the  subtrahend? 

What  is  the  whole  out  of  which  a  part  is  taken  ? 

10.  17+       ?==  25.-.  25  — 17=      ? 
What  number  added  to  17  equals  25  ? 
What  number  is  17  less  than  25  ? 

What  is  the  difference  between  25  and  17  ?    Between  25 
and  8? 


CHAPTER  TWO.  Ill 

LESSON    XXXVIII. 


2. 

2. 

6+     ?=13 

.-.13  — 

6= 

? 

7+ 

?=15 

.-.15  — 

7= 

? 

6+     ?=15 

.-.  15- 

6  = 

? 

7+ 

?=13 

.-.13- 

7  = 

9 

6+     ?=11 

.-.11- 

6  = 

9 

7+ 

?=16 

.-.16- 

7  = 

? 

6+     ?=14 

.-.14- 

6  = 

9 

7+ 

?=12 

.-.12- 

7= 

9 

6+     ? 

-10 

.-.10- 

6  = 

? 

7+ 

?=23 

.-.23  — 

1= 

? 

3. 

4. 

8+     ? 

=  13 

.-.13  — 

o  

? 

9+ 

?=13 

.-.13  — 

9= 

9 

8+     ? 

=  17 

.-.17- 

8= 

? 

9+ 

?=16 

.-.16- 

9= 

9 

8+     ?=16 

.-.16- 

8  = 

? 

9+ 

?=21 

.-.21- 

9= 

? 

8+     ? 

=  14 

.-.14- 

8  = 

? 

9+ 

?=17 

.-.17- 

9= 

9 

8+     ? 

=  15 

.-.15- 

8= 

? 

9+ 

?=15 

.-.15  — 

9= 

• 

5. 

6. 

7. 

18  less 

4? 

14 

less 

5? 

15 

less  7  ? 

13  less 

7? 

14 

less 

9? 

15 

less  9  ? 

13  less 

6? 

14 

less 

6? 

15 

less  8  ? 

13  less 

9? 

14 

less 

8? 

15 

less  6  ? 

13  less 

5? 

14 

less 

7? 

15 

less  two 

5's? 

13  less 

8? 

14 

less 

4? 

15 

less  three  4's  ? 

8. 

9. 

10. 

16  less 

7? 

17 

less 

8? 

18 

less  13  ? 

16  less 

9? 

17 

less 

9? 

-  18 

less  7  ? 

16  less 

5? 

17 

less 

7? 

18 

less  9? 

16  less 

8? 

17 

less 

two 

7's? 

18 

less  6  ? 

16  less 

three  5's? 

17 

less 

four 

4's? 

18 

less  8  + 

7? 

16  less 

four 

3's? 

17 

less 

5  +  6? 

18 

less  five 

3's? 

112  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XXXIX. 


z. 

21 

less 

9? 

2.  33 

less 

19? 

3. 

42  less 

5? 

21 

less 

13? 

33 

less  17  ? 

42  less 

7? 

21 

less 

17? 

33 

less 

15? 

42  less 

9? 

21 

less 

6? 

83 

less 

9? 

42  less 

13? 

21 

less 

8? 

33 

less 

7? 

42  less 

15? 

21 

less 

7? 

33 

less 

5? 

42  less 

17? 

rf. 

45 

less 

36? 

26? 

16? 

5. 

45  less  39? 

29? 

19? 

45 

less 

38? 

28? 

18? 

47 

less  38? 

28? 

18? 

45 

less 

34? 

24? 

14? 

53  less  47? 

37? 

27? 

45 

less 

37? 

27? 

17? 

61 

less  15? 

16? 

25? 

45 

less 

39? 

29? 

19? 

62 

less  18? 

14? 

28? 

45 

less 

33? 

23? 

13? 

62 

less  19? 

13? 

49? 

6. 

83 

less 

6? 

16? 

26? 

36? 

46? 

56? 

66?      76? 

88 

less 

4? 

14? 

24? 

34? 

44?      54? 

64?      74? 

83 

less 

8? 

18? 

28? 

38? 

48? 

58? 

68?      78? 

83 

less 

5? 

15? 

25? 

35? 

45?      55? 

65?      75? 

83 

less 

9? 

19? 

29? 

39? 

49? 

59? 

69?      79? 

83  less  7?  17?  27?  37?  47?  57?  67?   77? 

7.  72  less  3?  13?  23?  33?  43?  53?  63? 
72  less  4?  14?  24?  34?  44?  54?  64? 
72  less  5?  15?  25?  35?  45?  55?  65? 
72  less  7?  17?  27?  37?  47?  57?  67? 
72  less  8?  18?  28?  38?  48?  58?  68? 
72  less  9?  19?  29?  39?  49?  59?  69? 

8.  91  less  13?  43?  23?  83?  63?  33?  53?   73? 
91  less  24?  14?  84?  4?  74?  44?  64?   54? 
91  less  15?  85?  75?  5?  85?  45?  65?   55? 
91  less  36?  16?  86?  6?  26?  76?  46?   66? 
91  less  17?  37?  27?  47?  87?  57?  77?   67? 
91  less  18?  8?  48?  78?  68?  88?  28?   58? 


CHAPTER  TWO.  113 

LESSON    XL. 

1.  Find  the  difference  between  82  and  45. 

SUGGESTION  :  82  =  70  +  12 

45  =  40  +     5 

37=30^~7 

2.  Find  the  difference  between  : 

A  63  and  24.                1.  60  and  41.  1.  81  and  49. 

2.  75  and  19.                2.  70  and  22.  2.  63  and  27. 

3.  84  and  27.                3.  80  and  13.  3.  57  and  18. 

4.  92  and  35.                4.  90  and  54.  4.  74  and  35. 

5.  57  and  28.                 5.  98  and  29.  d.  93  and  56. 

6.  47  and  64.                 6.  19  and  66.  6.  82  and  47. 

7.  29  and  63.                 7.  23  and  71.  7.  67  and  39. 

8.  38  and  97.                8.  34  and  82.  8.  76  and  28. 
P.  26  and  85.                9.  41  and  90.  9.  63  and  44. 

10.  17  and  42.              10.  18  and  96.  10.  95  and  38. 

3.  From  420  subtract  124. 

SUGGESTION:  420  =  300  +  110+10 

134=100+     30+     4 

286  =  2OO  +80+6 

4.  Find  the  difference  between: 

1.  612  and  178.  1.  462  and  238.  1.  531  and  353. 

2.  523  and  164.  2.  374  and  257.  2.  642  and  265. 

3.  825  and  187.  3.  281  and  265.  3.  763  and  278. 

4.  417  and  158.  4.  592  and  283.  4.  824  and  297. 

5.  731  and  194.  5.  476  and  268.  5.  915  and  526. 

6.  324  and  165.  6.  852  and  239.  6.  812  and  355. 

7.  942  and  174.  7.  407  and  284.  7.  514  and  136. 

8.  635  and  189.  8.  308  and  275.  8.  972  and  479. 

9.  522  and  156.  9.  609  and  258.  9.  624  and  248. 

10.  417  and  168.  10.  205  and  81.  10.  512  and  247. 

11.  325  and  186.  11.  506  and  263.  11.  713  and  364. 

12.  712  and  194.  12.  807  and  442.  12.  817  and  528. 


FIRST  BOON  IN  ARITHMETIC. 

LESSON    XLI. 

1.  From  4000  subtract  1204. 

SUGGESTION:          4000  =  3000  +  90O  -f  90  -f-  1O 
1204  =  1OOO  -I-  200  +    0  +     4 


2796  =  2000  +  700  +  90  +     6 

2. 

3. 

4. 

5. 

From 

3273 

6345 

5702 

7465 

Subtract 

1423 

2462 

4384 

3270 

6. 

7. 

8. 

From 

42679  miles 

51062 

acres 

2467  feet 

Subtract 

14384     " 

24300 

H 

1803     " 

9.  Subtract  20762  from  53120. 

10.  Subtract  6472  rods  from  15200  rods. 


1.  From  $8  take  $2  and  68  cents. 

2.  From  $1  take  37  cents. 

3.  Subtract  $5  and  19  cents  from  $23. 

4.  Out  of  $3  take  87  cents. 

5.  $3.04  less  95  cents  equals  what? 

6.  Out  of  1  ton  take  1120  Bbs. 

7.  From  2  days  take  25  hours. 

8.  From    1    yard    measure   off  1   ft.    six  inches.     What 
remains  ? 

9.  From  the  month  of  June  deduct  ^  of  a  week. 

10.  From  500  Ibs.  take  4  cwt. 

11.  From  I  of  $420  take  }  of  $420. 

12.  From  £  of  720  pounds  take  %  of  720  pounds. 

13.  From  $12  take  12  cents. 

14.  From  $49  take  $.49. 

15.  From  15  yards  take  15  feet. 


CHAPTER  TWO. 


115 


LESSON    XLII. 

What  is  the 

difference 

between  : 

1. 

Three 

6's  and  two 

7's? 

2. 

Three 

7's  and  two 

8's? 

3. 

Three 

8's  and  two 

9's? 

4. 

Three 

9's  and  two 

10's? 

5. 

Four 

6's  and  three 

7's? 

6. 

Four 

7's  and  five 

5's? 

7. 

Four 

8's  and  six 

5's? 

8. 

Four 

9's  and  four 

7's? 

9. 

Six 

7's  and  four 

8's? 

10. 

Six 

8's  and  seven 

6's? 

11. 

Six 

9's  and  seven 

7's? 

12. 

Seven 

5's  and  four 

7's? 

13. 

Seven 

8's  and  nine 

6's? 

14. 

Seven 

9's  and  eight 

7's? 

15. 

Nine 

9's  and  eleven 

7's? 

16. 

Six 

8's  and  four 

12's? 

17. 

Three 

12's  and  four 

9's? 

18. 

Three 

6's  and  two 

9's? 

19. 

Eleven 

11  's  and  ten 

12's? 

20. 

Twelve 

10  's  and  nine 

9's? 

1.  A  man,  having  25  dollars  due  him,  received  a  ton  of  hay 
worth  11  dollars,  and  the  remainder  in  money.     How  much 
money  did  he  receive? 

2.  There  are  45  trees  in  an  orchard;  35  of  them  are  apple 
trees  and  the  remainder  peach  trees.     How  many  are  peach 
trees? 

3.  From  a  piece  of  hroadcloth  containing  27  yards,  15  yards 
were  cut?     How  many  yards  remained? 

4.  A  jeweler  bought  a  watch  for  60  dollars,  and  sold  it 
again  for  75  dollars?     How  much  did  he  gain? 

5.  The  number  of  pupils  registered  in  a  school  is  87;  6# 
are  present.     How  many  are  absent? 


116  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XLIII. 

1.  Charles  has  48  cents,  and  buys  a  slate  for  16   cents. 
How  many  cents  has  he  left? 

2.  A  farmer  sold  a  cow  for  22  dollars,  that  cost  him  30 
dollars.     How  much  did  he  lose  by  the  bargain? 

3.  A  grocer  bought  a  quantity  of  sugar  for  39  dollars,  and 
sold  it  for  50  dollars.     How  much  did  he  gain? 

4.  In  a  school  are  27  boys  and  35  girls.      How  many  more 
girls  than  boys? 

5.  A  man  died  at  the  age  of  77  years,  having  been  mar- 
ried 49  years.     What  was  his  age  when  he  married? 

6.  Martin  having  27  marbles  gave  12  to  Albert  and  lost  5. 
How  many  had  he  left? 

7.  Reuben  had  16  cents,  Charles  gave  him  10,  Elisha  gave 
him  9,  and  Henry  gave  him  enough  to  make  his  number  42. 
How  many  cents  did  Henry  give  him? 

8.  A  merchant  bought  a  hogshead  of  sugar  for  50  dollars; 
he  paid  6  dollars  for  freight  and  customs,  and  sold  the  whole 
for  75  dollars.     How  much  did  he  gain? 

9.  A  man  bought  a  watch  for  40  dollars,  a  chain  for  15  dol- 
lars, and  a  key  for  3  dollars,  and  he  sold  the  whole  for  50 
dollars.     How  much  did  he  lose  by  the  bargain? 

10.  Sarah  bought  a  comb  for  12  cents,  some  ribbon  for  16 
cents,  a  thimble  for  10  cents,  and  some  thread  for  6  cents. 
How  much  had  she  left  of  fifty  cents  after  paying  for  these 
articles? 

11.  A  drover  bought  9  sheep  of  one  man,  12  of  another,  and 
15  of  another;  he  afterwards  sold  8  and  butchered  5.     How 
many  had  he  left? 

12.  From  a  piece  of  calico  containing  26  yards  Jane  bought 
a  dress  of  5  yards,  and  Josephine  another  of  10  yards.     How 
many  yards  were  left  in  the  piece? 


CHAPTER   TWO.  117 

LESSON    XLIV. 

1.  Four  men  bought  a  horse  for  80  dollars,  the  first  gave 
25  dollars,  the  second  20  dollars,  and  the  third  18  dollars. 
How  much  did  the  fourth  give? 

2.  A  boy  had  12  marbles,  another  boy  gave  him  10  more, 
another  9,  and  another  enough  more  to  make  his  number  40. 
How  many  did  the  last  boy  give  him? 

3.  A  man  traveled  22  miles  one  day,  and  26  miles   the 
second  day,  and  on  the  third  day  he  traveled  30  miles  on  his 
return.     How  many  miles  was  he  from  the  place  from  which 
he  first  started? 

4.  George  sold  two  dozen  eggs  for  20  cents,  one  bushel  of 
apples  for  37  cents,  and  received  a  pair  of  skates  worth  75 
cents.     How  much  did  he  owe  for  his  skates? 

5.  A  man  owed  his  grocer  18  dollars,  his  tailor  20  dollars, 
and  a  merchant  25  dollars;  he  paid  the  grocer  10  dollars,  the 
tailor  12  dollars,  and  the  merchant  15  dollars.     How  much 
did  he  still  owe  them  all? 

6.  Bought  a  horse  for  90  dollars,  a  cutter  for  40  dollars,  and 
a  harness  for  20  dollars,  and  then  sold  the  whole  for  50  dol- 
lars more  than  the  horse  cost  me.     Did  I  gain  or  lose  by  the 
bargain,  and  how  much? 

7.  A  lady  bought  a  new  bonnet  for  7  dollars,  a  dress  for  12 
dollars,  a  pair  of  shoes  for  2  dollars,  and  a  parasol  for  3  dol- 
lars.    She  gave  the  merchant  3  ten  dollar  bills;  how  many 
dollars  must  be  returned? 

8.  A  tailor  bought  a  piece  of  cloth  containing  81  yards, 
from  which  he  sold  13  yards  to  one  man,  and  11  yards  to 
another.     How  many  yards  were  left  of  the  piece? 

9.  A  farmer  had  45  sheep  in  one  lot,  37  in  another,  and  30 
in  another.     From  the  first  he  sold  10,  from  the  second  15, 
and  from  the  third  11;  how  many  had  he  at  first,  and  how 
many  had  he  left? 


118  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XLV. 

1.  The  great  fire  in  Chicago  was  in  1871.     How  many 
years  since? 

2.  A  man  having  $2575.75,  gave  $1250  for  a  house,  and 
paid  $570.64  for  repairs.     How  much  had  he  left? 

3.  Two  men  bought  a  piece  of  property  for  $358.50.     One 
paid  $146.30.     How  much  did  the  other  pay? 

4.  A  farmer  raised  2584  bu.  of  wheat.     He  sold  800  bu.  to 
one  man,  and  1075  bu.  to  another.     How  many  bushels  had 
he  left? 

5.  If  a  man's  income  is  $175  a  month,  and  he  pays  $25 
for  rent,  $44  for  provisions,  and  $18  for  other  expenses,  how 
much  will  he  have  left? 

6.  George  Washington  was  born  in  the  year  1732,  and  died 
in  1799.     At  what  age  did  he  die? 

7.  Queen  Victoria  was  born  in  1819.    How  old  is  she?    She 
became  Queen  of  England  in  1837.     How  long  has  she  been 
a  queen? 

8.  What  number  must  be  added  to  4367  to  make  7210? 

9.  The  first  newspaper  published  in  America  was  issued  at 
Boston  in  1704.     How  many  years  since? 

10.  The  Brooklyn  Suspension  Bridge  was  commenced  in 
1869,  and  finished  in  1883.     How  long  was  it  in  building? 

11.  Bought  a  sack  of  flour  for  $1.75,  a  pound  of  tea  for 
$.90,  and  some  sugar  for  $2.25.     How  much  must  I  receive 
in  change  for  a  five-dollar  bill? 

12.  A  drover  bought  3245  sheep,  and  sold  1200  of  them. 
How  many  had  he  left? 

13.  A  speculator  gained  $5760,  and  afterward  lost  $2746; 
at  another  time  he  gained  $3575,  and  then  lost  $4632.     How 
much  did  his  gains  exceed  his  losses? 

14.  A  flour  merchant  bought  240  barrels  of  flour  for  $1920, 
and  sold  the  same  at  $10  a  barrel.     What  did  he  gain? 


CHAPTER  TWO.  119 

LESSON    XLVI. 

1.  A  lot  that  cost  $475  was  sold  for  $725.     What  was  the 
gain? 

2.  A  horse  that  cost  $315  was  sold  for  $268.     What  was 
the  loss? 

3.  If  I  give  $141  for  a  piece  of  cloth  containing  47  yards, 
for  how  much  must  I  sell  it  in  order  to  gain  one  dollar  a  yard? 

4.  A  speculator  who  owned  500  acres,  17  acres,  98  acres, 
and  121  acres  of  land,  sold  235  acres.     How  many  acres  had 
he  left? 

5.  A  dealer  sold  a  cargo  of  salt  for  $2300  and  gained  $625. 
What  did  the  cargo  cost  him? 

6.  The  art  of  printing  was  invented  in  1441.     How  many 
years  ago  was  it? 

7.  The  telescope  was  invented  in  1610.     How  many  years 
since  that  time? 

8.  Benj.  Franklin  died  at  the  age  of  84  in  1798.     In  what 
year  was  he  born? 

9.  America  was  discovered  in  1492.     How  many  years  ago? 

10.  American  Independence  dates  from  July  4,  1776.    How 
many  anniversaries  have  there  been? 

11.  Sir  Isaac  Newton  was  born  in  1642,  and  died  in  1727. 
What  was  his  age? 

12.  How  old  are  you?    From  your  age  find  in  what  year 
you  were  born? 

13.  It  is  now  Tuesday  noon.    How  long  is  it  since  9  o'clock 
A.  M.  of  yesterday? 

14.  How  old  is  a  man  in  1885  who  was  born  in  1837? 

15.  In  what  year  was  a  man  born  who  is  now  92  years  of  age? 

16.  Figures  were  used  by  the  Arabs  in  the  year  890.    How 
long  ago? 

17.  Decimal  fractions  were  invented  in  1464.     How  long 
since? 


120  FIRST  BOOK  IN  ARITHMETIC. 


LESSON    XLVIL 

1.  From  6438  subtract  the  sum  of  2304,  983,  46  and  8. 
SUGGESTION: 

Minuend,               6438  Write  the  numbers  as  in  addition. 

{2304  Connect  the  numbers  of  the  subtra- 

983  hend  by  a  brace.     Add  the  columns 

46  of  the  subtrahend  thus:   8,  14,  17, 

8  21,  and  7  are  28.     Write  7  in  the 

Or.or7  difference.)      2,  6,  14,  and   9  are 

ifference,               >97  23      (Write9inthedifference>)    2> 

11,  14.     (Write  zero  in  the  difference.)    1,  3,  and  3  are  6.     (Write 
3  in  the  difference.) 


Min. 
Sub. 


2. 

3. 

4. 

5. 

6. 

7862 

18344 

29460 

44444  Ibs. 

$764.90 

1646 

C  6462 

(  17340 

(  2222  Ibs. 

(  $250.40 

876 

1  4366 

}  3460 

1  3333  Ibs. 

<  164.50 

49 

(  868 

(   580 

(  5555  Ibs. 

(   75.19 

7.  The  sum  of  three  numbers  is  90090.     Two  of  them  are 
50050  and  6606.     What  is  the  third  number? 

8.  A  man  left  $50000  to  his  wife,  two  sons,  and  daughter. 
To  his  wife,  $20000;   to  each  of  his  sons,  $12500.     What 
was  the  daughter's  portion? 

9.  A  man  owed  $12500  on  his  house.     After  making  three 
3000  dollar  payments  and  one  payment  of  $2650,  how  much 
did  he  owe? 

10.  A  suburban  gentleman  bought  a  1000-mile  railroad 
ticket  for  family  use.  His  wife  rode  140  miles,  his  son  124 
miles,  his  daughter  168  miles  and  the  gentleman  himself  the 
remainder.  How  many  miles  did  the  gentleman  ride? 

11.  A  man  bought  four  city  lots,  for  which  he  paid  $15760. 
For  the  first  he  paid  $2175,  for  the  second  $3794,  and  for  the 
third  $4587.  How  much  did  he  pay  for  the  fourth? 


CHAPTER  TWO.  121 

LESSON    XLVIII. 

1.  Paid  $979  for  a  lot  and  $7560  for  the  house  on  it.     How 
much  more  did  the  house  cost  than  the  lot? 

2.  A  gentleman's  income  is  $7560  a  year.     How  much  may 
he  save  if  his  expenses  are  $3928? 

3.  A  man  bought  a  farm  for  $12500,  and  sold  it  at  a  ]oss 
of  $3856.     What  was  the  selling  price? 

4.  A  man  has  property  worth   $31567,  and  owes  $19708. 
How  much  will  he  have  after  paying  his  debts? 

5.  A  merchant  had  deposited  in  bank  $9723.     How  much 
had  he  left  in  bank  after  drawing  out  enough  to  pay  a  bill  of 
$2757? 

6.  A  has  property  worth  $17250,  which  is    $3980  more 
than  the  value  of  B's  property.      What  is  the  value  of  B's 
property? 

7.  A  gardener  received  one  year  for  the  fruits  and  vege- 
tables he  raised  $4125,  and  his  expenses  were  $2739.     How 
much  were  his  profits? 

8.  A  man  who  has  $7580,  lacks  how    much   of   having 
enough  to  buy  a  farm  worth  $10000? 

9.  What  amount  taken  from  $21819  will  leave  $17963? 

10.  What    amount  must   be    added    to    $9562   to   make 
$10000. 

1.  6846  —  4908.  10.  From  $1  take  1  cent. 

2.  3000  —  1018.  11.  From  $2  take  18  cents. 

3.  844  —    266.  12.  From  $3  take  $1.12. 

4.  5641  —  2673.  13.  From  $4  take  $2.07. 

5.  800  -      161.  14.  From  $5  take  $2.10. 
e.  6005  —      27.                 15.  From  $6  take  $4.90. 

7.  4231  —    868.  16.  From  $7  take  $3.09. 

8.  2372  —  1466.  17.  Form  $8  take  $4.40. 
p.  8000  —    111.                18.  From  $9  take  $6.27. 


122  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XLIX. 

MULTIPLICATION. 

1.  How  many  trees  are  there  in  8  rows  of  9  trees  each? 
This  is  a  question  of  Multiplication. 

ANALYSIS.  In  8  rows  there  are  8  times  as  many  trees  as  in  1 
row.  There  are,  therefore,  8  times  9  trees,  or  a  number  of  trees 
equal  to  eight  9's.  You  have  learned  that  eight  9's  are  72.  And  8 
times  9  trees  are  72  trees. 

2.  In  the  example,  9  (the  number  of  trees  in  each  row)  is 
the  Multiplicand. 

3.  8  (the  number  of  rows)  is  the  Multiplier. 

4.  72  (the  number  of  trees  in  8  rows)  is  the  Product. 

SUGGESTION:  The  product,  like  the  multiplicand,  is  a  number  of 
trees. 

5.  The  operation  of   combining  numbers  to   obtain   their 
product  is  Multiplication. 

6.  The  multiplicand  and   multiplier  are  sometimes  called 
Factors  of  the  product.     Thus  :  3  and  5  are  factors  of  15; 
3  and  17  are  factors  of  51;  3,  4  and  5  are  factors  of  60. 

7.  What  will  6  horses  cost  at  $125  each? 
What  is  the  multiplicand?     $125. 
What  is  the  multiplier?     6  ones. 

What  is  the  product?  A  number  of  dollars  equal  to  six 
125's. 

8.  21=  -I tbree  7>s  I  What  are  the  factors  of  21? 

(  seven  3  s  ) 

9.  45=  \  five     9's  i  What  are  the  factors  of  45? 

(  nine   5's  ) 

10.  63=  J  seven  9's  i  What  are  the  factors  of  63? 
(  nine   7s  ) 


CHAPTER  TWO.  123 

LESSON    L. 


Find  products 

1. 
2. 
3. 

80  mi. 
6 

40  mi. 
6 

SOT. 

7 

60  mi. 
6 

50  T. 

7 

80  mi. 
6 

40  T. 

7 

60  T. 

7 

90  T. 

7 

$50 
8 

|80 
8 

$60 
8 

$90 
8 

$70  . 
8 

4. 
5. 

60  bu. 
9 

70  bu. 
9 

50  bu. 
9 

90  bu. 
9 

80  bu. 
9 

25 
6 

36 
6 

47 
6 

58 
6 

69 
6 

6. 

44 

7 

64 

7 

74 

7 

84 

7 

94 

7 

7. 

56 
8 

66 

8 

76 
8 

86 
8 

96 

8 

8. 

63 
9 

43 
9 

73 
9 

83 
9 

93 
9 

9. 

48 
11 

77 
11 

73 
11 

56 
12 

94 
12 

.10. 

99 
6 

88 
7 

66 
9 

55 
11 

90 
12 

124  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    LI. 

1.  What  is  the  cost  of  4  lots  at  $250  each? 

SOLUTION: 
By  addition: 

$250  The  cost  of  the  4  lots  is  the  sum  of    $250, 

250          written  as  many  times  as  there  are  lots,  as  shown 
250          in  the  margin. 
250 


Sum.   $1000 

By  multiplication : 

The  same  result  is  obtained  by  writing  $250 
$250    once  and  multiplying  by  4.    The  operation  may 

4    be  recited  thus  :     4  50's  are  200;    4  200's  are 

Product.  $1000    800.     800+200=1000. 

It  will  be  seen  that  the  product  is  obtained  with  fewer  figures 
than  the  sum. 

Multiplication  is  a  short  way  of  obtaining  results  in  addition  by 
means  of  memorized  facts  of  addition. 

Without  a  previous  knowledge  of  addition,  no  multiplication  is 
possible. 

323     444     555     666     345 
2.     6       6       6       6       6 


444  555  616  456  634 

3.  1       7  7  7  7 

558  680  790  912  888 

4.  8                8  8  8  8 

548  654  765  876  987 

5.  9                9  9  9  9 


CHAPTER  TWO.  .          125 

LESSON    LII. 

Find  products : 

1.  $     4.80  $  42.10  $  18.40  $     11.44 

6789 


2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
11. 
12. 

16  rds.  2  ft. 
6 

19  rds.  5  yds, 

7 

25  mi.  10  rds. 
8 

6  ft.  6  in. 
9 

$  81.92 
6 

$  21.70 

7 

$  15.15 

8 

$  18.19 
9 

40  yrs.  50  ds. 
6 

7  wks.  7  ds. 

7 

25  h.  5  min. 
8 

9  min.  6  sec. 
9 

$  74.06 
6 

$  38.09 

7 

$  57.64 
8 

$  32.58 
9 

$100.50 
6- 

$200.50 

7 

$500.25 
8 

$1000.75 
9 

8708 
6 

7608 

7 

9107 

8 

4808 
9 

$  9.06 
6 

$  8.09 

7 

$  7.05 
8 

$  6.08 
9 

$  2.20 
11 

$  3.30 
11 

$  4.40 
11 

$  5.50 
11 

$  1.20 
12 

$  6.06 
12 

$  8.08 
12 

$  9.09 
12 

440  min. 
12 

640  min. 
11 

320  rds. 
12 

365  min. 
11 

$  60.60 
9 

$500.05 
12 

$606.60 
9 

$  50.50 
12 

126  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    LIII. 

1.  At  6  cents  a  pound,  what  cost  675  pounds  of  rice? 

2.  At  $5.37  a  yard,  what  is  the  cost  of  7  yards  of  cloth? 

3.  At  $  124.50  an  acre,  what  will  5  acres  of  land  cost? 

4.  What  is  the  cost  of  8  building  lots,  at  $2015  each? 

5.  What  cost  326  tons  of  coal  at  $6  a  ton? 

6.  What  cost  1238  cords  of  wood  at  $5  a  cord? 

7.  What  cost  752  pounds  of  nails,  at  7  cents  a  pound? 

8.  What  cost  2140  barrels  of  flour  at  $8  a  barrel? 

9.  What  cost  379  pounds  of  nails  at  6  cents  a  pound? 

10.  At  9  cents '  a  pound,  what  will  1872  pounds  of  sugar 
cost? 

11.  At  $98  a  month  how  much   can  a  man  earn  in  8 
months. 

12.  At  $6.75  what  will  7  tons  of  coal  cost? 

13.  What  are  514  barrels  of  apples  worth  at  $4  a  barrel? 
At  $5?    At  $7? 

14.  What  cost  3250  pounds  of  pork  at  6  cents  a  pound? 
At  8  cents?     At  9  cents? 

15.  In  one  day  there  are  1440  minutes.     How  many  min- 
utes in  9  days? 

16.  1  mile=5280  feet.     How  many  feet  in  8  miles? 

17.  1  year =8760  hours.     How  many  hours  in  6  years? 

18.  1760  yards  =  1  mile.     How  many  yards  in  7  miles? 

19.  If  an  army  consumes  5763  barrels  of  flour  a  week,  how 
many  barrels  will  last  the  army  8  weeks? 

20.  If  the  profits  of  a  mill  are  $3750  a  year,  what  will  be 
the  profits  for  five  years? 

21.  What  would  113  plows  cost  at  $11  each? 

22.  How  many  inches  are  there  in  460  feet? 

23.  How  many  pecks  are  there  in  1280  bushels? 

24.  How  many  pounds  are  therein  15  tons? 

25.  At  75  cents  a  pound,  what  is  the  cost  of  9  Ibs.  of  tea? 


CHAPTER  TWO.  127 

LESSON    LIV. 

1.  At  $6  a  ton  for  coal,  what  will  10  tons  cost?     100  tons? 
1000  tons? 

SUGGESTION: 

When  the  product  can  be  written  at  sight,  the 
$6X  10=$  60  form  of  an  equation  should  be  used  in  multi- 
$6  X  100=  $  600  plication,  instead  of  the  usual  form  of  writing 
$6X1000=  $600.0  the  multiplier  under  the  multiplicand.  Ob- 
serve that,  in  the  product  by  10,  the  figure  of  the  multiplicand  is  writ- 
ten one  place  to  the  left;  by  100,  two  places;  by  1000,  three  places. 

2.  At  $5  per  barrel,  what  is  the  cost  of  100  barrels  of  apples? 

3.  At  $16.80  a  ton,  what  sum  of  money  will  purchase  1000 
tons  of  hay? 

4.  At  $215  a  share,  what  do  100  shares  of  city  railway 
stock  cost? 

5.  Multiply  $25.50  by  10,  100,  300,  and  add  the  products. 

6.  How  many  cents  are  there  in  $60? 

7.  How  many  pounds  are  there  in  20  hundred  weight? 

8.  How  many  days  have  there  been  in  the  months  of  Jan- 
uary for  the  last  100  years? 

9.  Multiply  5  cents  by  10,  100,  and  1000,  and  add  the  pro- 
ducts. 

10.  At  $50  a  head  what  cost  100  head  of  cattle? 

1.  What  is  a  farm  of  500  acres  worth  at  $300  an  acre? 
$300X500=$150000. 

SUGGESTION:       300=    3x100 
500=    5x100 


150000  =  15X10000 

2.  Multiply  1200  by  60. 

3.  Multiply  900  by  80. 

4.  Multiply  $1200  by  120. 

5.  Multiply  90  pounds  by  110. 

6.  Multiply  $18.185  by  2000. 


128  FIRST  BOOK  IN  ARITHMETIC. 

LESSON  LV. 

1.  Multiply  476  by  43. 

SUGGESTION: 

40=   4X10. 
43  43  =  40+  3. 

1428= product  by  3.  We  multiP1y  ^  43  b?  multi~ 

.          '  plying  first  by  3  and  then  by  4 

1904  =product  by  40.  and  adding  the   two  productg. 

20468= product  by  43.  But  because  the  4  is  4  tens  or 

4  X 10  we  write  the  second  pro- 
duct one  place  to  the  left  of  the  first  product,  since  to  multiply  by 
10  is  to  remove  the  figures  so  multiplied  one  place  to  the  left. 

2.  Multiply     4732  by  36.  7.  Multiply    5684  by  96. 

3.  Multiply     8721  by  47.  8.  Multiply  $2460  by  76. 

4.  Multiply     7648  by  54.  9.  Multiply  $2850  by  69. 

5.  Multiply    3472  by  48.  10.  Multiply  $826  by  75. 

6.  Multiply  14761  by  83. 

11.  At  $156  each,  what  is  the  value  of  34  wagons? 

12.  What  cost  297  tons  of  iron  at  $27  per  ton? 

13.  A  miller  filled  398  sacks  with  flour,  putting  49  pounds 
in  each.     How  many  pounds  were  required? 

14.  A  canal  38  miles  long  cost  $2476  per  mile.     What  was 
the  whole  cost? 

15.  How  many  yards^  in  76  pieces  of  muslin,  each  contain- 
ing 39  yards? 

16.  A.  barrel  of  flour  contains  196   pounds.     How   many 
pounds  in  98  barrels? 

17.  Mr.  Jones  paid  $68  per  acre  for  his  farm  of.  385  acres. 
What  did  the  farm  cost? 

18.  There  are  320  rods  in  a  mile.     How  many  rods  in  27 
miles? 

19.  How  many  pounds  in  87  bales  of  cotton,  each  weighing 
497  pounds? 

20.  How  many  days  in  65  years  of  365  days  each? 


CHAPTER  TWO.  129 

LESSON    LVI. 

1.  Multiply  458  by  15;  by  51. 

458  Xl5.  SUGGESTION: 

2290= product  by    5.  15  =  10+5. 

6870=product  by  15.  51  =  50+1, 

458x51.  Inspect  operation  in  the  mar- 

2290  =  product  by  50.  gin  for  explanation. 

23358 ^product  by  51. 

2.  Multiply  4865  by  13;  by  17;  by  19. 

3.  Multiply  5780  by  31;  by  71;  by  91. 

4.  How  many  days  in  18  years  of  365  days  each? 

5.  How  many  Ibs.  in  61  bbls.  of  flour,  each  bbl.  containing 
196  Ibs. 

6.  Multiply  456  by  374;  by  608. 

AKQ  SUGGESTION: 

374  374  =  300+70+4. 

We  multiply  456  by  4,  7  and 

1824=product  by      4.  3. 

3192  ^product  by    70.  In  writing  the  product  by  7 

1368     ^product  by  300.  multiply  by  10. 

In  writing  the   product  by  3 

170544=product  by  374.  multiply  by  100. 

456 

603  SUGGESTION: 

Inspect  the  operation  in  the 


3648=product  by  8.  margin> 

2736 = product  by  600.  Explain  the  placing  of  the  pro- 

277248=product  by  608.         duct  by  6* 


130  FIRST  BOOK  IN  ARITHMETIC. 


LESSON    LVII. 

1.  408x325  11.     5800x643  21.  8481x820 

2.  908x625  12.     7059x297  22.  4308x398 

3.  794x793  13.     9000x580  23.  2909x756 

4.  896x528  14.  11415x584  24.  5941x400 

5.  1407x412  15.  3623x379  25.  2597x680. 

6.  2316x700  16.  5856x298  26.  6271x809 

7.  7543x256  17.  7958x563  27.  7039x297 

8.  9127x700  18.  3758x460  28.  3781x397 

9.  7658x850  19.  8080x597  29.  5870x563 
10.  5397x809  20.  9086x790  30.  9205x643 

1.  How  many  days  in  129  years,  counting  365  days  as  1 
year? 

2.  There  are  144  square  inches  in  a  square  foot;  how  many 
square  inches  in  576  square  feet? 

3.  How  many  pages  in  438  books,  if  there  are  364  pages 
in  each? 

4.  There  are  160  square  rods  in  an  acre;  how  many  square 
rods  in  a  farm  of  267  acres? 

5.  A  steamer  had  a  cargo  of  516  bales  of  cotton,  the  aver- 
age weight  of  each  bale  being  438  pounds;  what  was  the 
entire  weight  of  the  cargo? 

6.  There  are  2000  pounds  in  a  ton ;  how  many  pounds  in 
234  tons? 

7.  There  are  1760  yards  in  a  mile.     How  many  yards  in 
416  miles? 

8.  A  factory  makes  1750  boxes  of   matches  a  day.     How 
many  will  it  make  in  a  year  of  312  days? 

9.  The  multiplicand  is  $756,  the  multiplier  is  418.     What 
is  the  product? 

10.  A  man  bought  45  acres  of  land  at  $38  an  acre,  and  76 
acres  at  $47  an  acre,  and  sold  the  whole  at  $45  an  acre.    Did 
he  gain  or  lose,  and  how  much? 

11.  A  farmer  exchanged  584  bushels  of  wheat  at  $2   a 
bushel,  for  78  barrels  of  flour  at  $9  a  barrel,  and  received  the 
balance  in  money.     How  much  money  did  he  receive? 


CHAPTER  TWO.  131 

LESSON    LVIII. 

1.  How  many  pounds  of  coal  in  100  tons? 

2.  Cost  of  500  barrels  of  flour  at  $5.50  per  barrel? 

3.  Cost  of  7  thousand  feet  of  lumber  at  18  cents  a  foot? 

4.  How  many  feet  are  there  in  500  miles? 

5.  A  man  will  travel  how  many  miles  in  74  days,  at  the 
rate  of  37  miles  a  day? 

6.  What  was  the  cost  of  a  drove  of  257  head  of  cattle,  if 
the  average  price  was  $36  per  head? 

7.  1760  yards  make  a  mile,  36  inches  make  a  yard.     How 
many  inches  in  a  mile? 

8.  If  pork  is  worth  $27  per  bbl.,  how  much  will  386  bbls. 
cost? 

9.  Sold  267  tons  of  hay  at  $19  per  ton.     What  was  the 
amount  of  the  sale  ? 

10.  Two  persons  start  from  the  same  point  and  travel  in 
opposite  directions;  one  travels  at  the  rate  of  32  miles  a  day, 
the  other  at  the  rate  of  39  miles  a  day.     How  far  apart  will 
they  be  in  14  days? 

11.  A  man  bought  two  farms;  one  of  157  acres  at  $26  an 
acre,  and  another  of  138  acres  at  $34  an  acre.     He  paid  at 
one  time  $4725,  and  at  another  $1895.     How  much  remained 
unpaid  ? 

Multiply 

12.  2464  ft.  by  308.  21.  625x625. 

13.  2240  Ibs.  by  506.  22.  128x128. 

14.  1728  in.  by  144.  23.  640x640. 

15.  5380  ft.  by  300.  24.  144x144. 

16.  4080  days* by  1440.  25.  Ill  x  HI. 

17.  $108.60  by  640.  26.  121x121. 

18.  $270.75  by  709.  27.  221x221. 

19.  7623  bbls.  by  196.  28.  909  X  909. 

20.  5760  Ibs.  by  112.  29.  815x815. 


132  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    LIX. 

1.  A  farmer  owned  5  farms  of  160  acres  each.     How  much 
land  did  he  own? 

2.  He  set  apart  86  acres  from  each  farm  for  the  raising  of 
wheat.      His  wheat-yield  averaged  18  bushels  to  the  acre. 
How  much  wheat  did  he  raise? 

3.  He  sold  his  wheat  for  92  cents  a  hushel.     What  did  he 
receive  for  his  wheat? 

4.  He  planted  45   acres   of  each  farm   with  corn,  which 
yielded  32  bushels  to  the  acre.     How  much  corn  did  he  raise? 

6.  He  sold  his  corn  for  48  cents  a  bushel.      What  did  his 
corn  come  to? 

6.  If,  instead  of  selling  his  corn,  he  had  fed  it  to  hogs  and 
had  sold  his  hogs  for  $4500,  how  much  better  off  would  he 
have  been? 

7.  Other  portions  of  his  land  produced  hay  and  oats,  which 
he  fed  to  horses,  cattle  and  sheep.     He  sold  3  horses  for  $175 
each,  20  steers  for  $60  each.     He  made  1200  pounds  of  but- 
ter which  he   sold  at  23  cents  a  pound.     He  sheared  2400 
pounds  of  wool  which  he  sold  for  31  cents  a  pound.     What 
was  his  entire  income  from  his  5  farms? 

8.  If  his  first  farm  cost  him  $58  an  acre;  his  second,  $65; 
his  third,  $76;  his  fourth,  $87;  his  fifth  $113,  what  did  his 
land  cost  him? 

9.  If  he  sell  it  at  $13  an  acre  more  than  it  cost  him,  what 
will  he  receive  for  his  land? 

10.  If  the  farmer,  with  a  harvester,  could  do  the  work  of  5 
men  during  wheat  harvest,  what  would  the  harvester  be  worth 
to  him  during  a  harvest  of  20  days  when  labor  is  worth  $2.50 
a  day? 

11.  A  merchant  bought  29  pieces  of  cloth,  each  piece  con- 
taining 47  yards,  at  $8  a  yard.     Find  cost. 

12.  What  cost  45  sets  of  cyclopaedias,  each  set  containing 
16  volumes,  at  $7  a  volume? 

13.  How  many  yards  of  sheeting  in  57  bales,  each  bale  con- 
taining 26  pieces,  and  each  piece  44  yards? 


CHAPTER  TWO.  133 

LESSON    LX. 

1.  How  many  minutes  in  April,  June  and  November? 

2.  How  many  minutes  in  the  summer  months? 

3.  Cost  of  3  miles  of  telegraph  wire  at  3  cents  a  foot? 

4.  In  3  tons  of  cheese  now  many  pounds? 

5.  How  many  quarts  do  a  bushel,  a  half  bushel  and  a  peck 
measure  contain? 

6.  Bought  45  yards  of  cloth  and  sold  69  feet  of  it.     How 
many  yards  remained?    How  many  feet? 

7.  What  is  the  difference  between  3  pecks  and  7  quarts? 

8.  How  many  times  can  a  peck  measure  be  filled  from  a 
two-bushel  and  a  half -bushel  measure? 

9.  How  many  pounds  in  1  of  a  ton? 

10.  How  many  quarts  in  1  of  a  bushel? 

11.  How  many  inches  in  1  of  a  yard? 

12.  How  many  minutes  in  i  of  a  day? 

13.  How  many  rods  in  1  of  a  mile? 

14.  How  many  pints  in  3  pecks  and  2  quarts? 

15.  What  will  2  pecks  of  plums  cost  at  20  cents  a  quart? 

16.  At  5  cents  a  pint  what  is  a  bushel  of  chestnuts  worth? 

17.  From  a  barrel  containing  42  gallons,  10  gallons  and  2 
quarts  were  drawn.     How  many  quarts  remained? 

18.  How  many  half -pint  glasses  can  your  mother  fill  from 
6  quarts  of  jelly? 

19.  Change  2  yards  2  feet  to  inches. 

20.  Change  3  bushels  3  pecks  to  quarts. 

21.  At  4  cents  a  pint  for  milk,  what  is  the  price  per  gallon? 

22.  At  $9  a  yard  for  silk,  what  will  *  of  a  yard  cost? 

23.  Cost  of  101  Ibs.  of  sugar  at  6  cents  a  pound? 

24.  Cost  of  91  Ibs.  of  butter  at  12  cents  a  pound? 

25.  What  will  -Jy  of  22  yards  of  carpet  cost  at  $  1  a  yard? 

26.  If  10  Ibs.  of  butter  cost  $2.50,  what  does  \  of  a  Ib.  cost? 


134  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    LXI. 

DIVISION. 

1.  At  $7  a  ton,  how  many  tons  of  coal  can  be  bought 
for  $63? 

2.  If  $63  are  paid  for  9  tons  of  coal,  what  is  the  price  of 
one  ton? 

These  are  questions  of  division,  since  the  number  63  is  to 
be  divided  or  separated  into  parts. 

In  the  first  example  the  question  is,  how  many  7's  in  63,  or 
how  many  times  is  7  contained  in  63. 

In  the  second,  the  question  is,  what  is  one  of  the  nine  equal 
parts  of  63. 

3.  The  operation  of  finding  how  many  times  one  number  is 
contained  in  another  of  the  same  kind,  or  of  finding  one  of 
the  equal  parts  of  a  number  is  Division. 

4.  The  number  divided  is  called  Dividend. 

5.  The  number  by  which  we  divide  is  called  Divisor. 

6.  The  result  obtained  by  dividing  dividend  by  divisor  is 
called  Quotient. 

7.  Any  part  of  a  dividend  that  cannot  be  divided  is  called 
Remainder. 

8.  The  divisor  and  quotient  are  factors  of  the  dividend. 

SUGGESTION  TO  THE  TEACHER  :  Let  every  dividend  be  con- 
ceived of  as  having  had  a  previous  existence  as  a  product.  Keferring 
again  to  the  examples  given,  the  dividend  $63  was  obtained  as  a 
product.  The  divisor  ($7),  in  the  first  example,  was  the  multipli- 
cand. The  divisor  (9),  in  the  second,  was  the  multiplier. 

Inference:  When  the  dividend  and  divisor  are  alike,  the  product 
and  multiplicand  are  given  to  find  multiplier,  and  the  language  is, 
how  many  times.  When  the  dividend  and  divisor  are  unlike,  the 
product  and  multiplier  are  given  to  find  multiplicand,  and  the  lan- 
guage is,  what  is  one  of  the  equal  parts. 


CHAPTER  TWO.  135 

LESSON   LXIL 

1.  How  many  barrels,  each  holding  3  bushels,  will  be 
required  for  18  bushels  of  apples?     21  bushels? 

2.  How  many  times  can  6  yards  of  cloth  be  measured  from 
a  piece  containing  30  yards? 

3.  How  many  times  can  6  cents  be  taken  from  23  cents  so 
as  to  have  5  cents  remaining? 

4.  Distribute  $28  equally  among  7  men.     How  many  dol- 
lars will  each  receive? 

5.  How  do  you  find  one  of  8  equal  parts  of  a  number?     Of 
9  equal  parts?     Of  0  equal  parts? 

6.  What  is  one  of  4  equal  parts  of  40?    Of  36?     Of  48? 

7.  What  is  one  of  6  equal  parts  of  30?    Of  42?  of  48? 

8.  What  is  one  of  7  equal  parts  of  56  pounds? 

9.  How  many  times  8  cents  are  48  cents? 

10.  What  is  one  of  8  equal  parts  of  48  cents? 

11.  If  6  men  earn  24  dollars,  what  part  of  24  dollars  does 
1  man  earn?     How  many  dollars? 

12.  At  9  cents  a  quart,  how  many  quarts  of  milk  can  be 
bought  for  63  cents? 

13.  How  do  the  solutions  of  the  last  two  examples  differ? 

14.  How  many  yards  of  cloth,  at  7  dollars  a  yard,  can  be 
bought  for  70  dollars?     For  63  dollars?     For  84  dollars? 

15.  If  you  divide  84  cents  among  7  children,  what  part  of 
the  whole  do  you  give  to  each?     How  many  cents? 

16.  A.  farmer  gathered  108  bushels  of  apples  from  9  trees? 
What  was  the  average  number  of  bushels  to  each  tree? 

17.  A.  merchant  paid  $96  for  8  pieces  of  dress  goods.  What 
was  the  cost  of  each  piece? 

18.  If  a  farm  of  120  acres  is  divided  into  12  equal  lots, 
how  many  acres  does  each  lot  contain? 

19.  A.  roll  of  carpet  contains  88  yards.     Into  how  many 
pieces  of  11  yards  each  can  it  be  cut? 


136 


FIRST  BOOK  IN  ARITHMETIC. 


LESSON      LXIII. 


SUGGESTION:    $48-r-$8  =  48  are  how  many  8's? 

,    $48-^8    =iof$48. 

1. 

63  pecks    - 

-    9  pecks    equals  how  many? 

63  pecks    - 

-     9              equals  how  many  pecks? 

2. 

72  hours   - 

-    6  hours    equals  how  many? 

72  hours    - 

-    6              equals  how  many  hours? 

3. 

$120 

-    $12          equals  how  many  ? 

$120 

6          equals  how  many  dollars? 

4. 

108  quarts  - 

-    9  quarts  equals  how  many? 

108  quarts  - 

-  12               equals  how  many  quarts? 

5. 

49  days 

-    7  days      equals  how  many? 

49  days 

-     7               equals  how  many  days? 

6. 

56  bbls.     - 

-    8  bbls.     equals  how  many? 

56  bbls.     - 

-    7              equals  how  many  barrels? 

7. 

132  miles    - 

-12  miles    equals  how  many? 

132  miles    - 

-11               equals  how  many  miles? 

8. 

121  acres    - 

-11  acres    equals  how  many? 

121  acres    - 

-11              equals  how  many  acres? 

9. 

$54 

-  $9             equals  how  many? 

$54 

-    6              equals  how  many  dollars? 

10. 

42  quarts  - 

-    7  quarts  equals  how  many? 

42  quarts  - 

-    6              equals  how  many  quarts? 

11. 

84  rods      - 

-    7  rods     equals  how  many? 

84  rods     - 

-    6              equals  how  many  rods? 

12. 

45  weeks  - 

-    7  weeks  equals  how  many? 

45  weeks  - 

-    7  weeks  equals  how  many  weeks? 

13. 

$91 

-  $7             equals  how  many? 

$91 

-    7              equals  how  many  dollars? 

14. 

78  A 

-    6  A          equals  how  many? 

78  A 

-    6              equals  how  many  A? 

15. 

104  lots 

-    8  lots      equals  how  many? 

104  lots       - 

-    8              equals  how  many  lots? 

16. 

144  dozen   - 

-12  dozen  equals  how  many? 

144  dozen  -r-  12              equals  how  many  dozen? 

CHAPTER  TWO.  137 

LESSON  LXIV. 

1.  How  long  would  it  take  6  men  to  do  the  work  that  8 
men  do  in  9  days? 

2.  How  long  would  it  take  3  men  to  do  what  12  men  can 
do  in  8  days? 

8.  When  papers  cost  at  the  rate  of  24  cents  for  8  and  are 
sold  at  the  rate  of  60  cents  for  12,  how  many  papers  must  a 
boy  sell  in  a  week  to  make  30  cents  a  day? 

4.  Harper's  magazine  sells  for  35  cents.     If  the  newsdealer 
pays  28  cents,  how  many  must  he  sell  to  make  $5.60  profit? 

5.  If  his  profit  on  Harper's  is  $3.60  each  month,  how  many 
does  he  sell  in  a  year? 

6.  Potatoes  that  cost  50  cents  a  bushel  are  sold  at  15  cents 
a  peck.     How  many  bushels  thus  bought  and  sold  will  realize 
to  the  dealer  a  profit  of  $5?     $10?     $15? 

7.  If  gloves  that  cost  $36  a  dozen  pairs  are  sold  for  $42, 
what  is  the  profit  on  one  pair? 

8.  At  the  rate  of  3  pencils  for  11  cents,  what  is  the  price 
per  dozen? 

9.  If  8  pineapples  cost  $1,  what  will  6  dozen  pineapples 
cost? 

10.  When  corn  is  purchased  at  the  rate  of  7  bushels  for 
$4.20  and  sold  at  the  rate  of  6  bushels  for  $4.80,  how  many 
bushels  thus  bought  and  sold  would  yield  a  profit  of  $40? 
$60?     $80.80. 

11.  How  many  barrels  of  apples  worth  $3  a  barrel  would 
pay  for  7  tons  of  coal  at  $6  a  ton? 

12.  How  many  pounds  of  butter,  worth  20  cents  a  pound, 
would  pay  a  store  bill  of  $10? 

13.  At  4  cents  a  piece  for  oranges,  how  many  can  be  bought 
for  I  of  $1.20? 

14.  7  barrels  of  flour  are  worth  $56.     How  many  barrels 
of  sweet  potatoes,  worth  $3  a  barrel,  would  be  worth  as  much 
as  3  barrels  of  flour? 

15.  If  8  spring  chickens  are  worth  $1,  what  are  a  dozen 
worth? 


138 


FIRST  BOOK  IN  ARITHMETIC. 


LESSON     LXV. 


6x3= 

.-.18- 

-  6  = 

6x11  = 

.-.    66- 

-11 

18- 

-  3  = 

66- 

-  6 

7X3  = 

.-.21- 

rr  

7x   8  = 

.-.    56- 

-     8  = 

21- 

-  3  = 

56- 

-     7  = 

8x3  = 

.-.24- 

-  8  = 

7X   9  = 

.-.    63- 

-      9 

24- 

—  3  = 

63- 

-  7 

9x3  = 

.-.27- 

-  9= 

9x   5  = 

.-.    45- 

-  9 

27- 

-    3=: 

45- 

-  5 

6X4  = 

.-.24- 

-  6  = 

9x11  = 

.-.    99- 
99- 

-11 
-  9 

24- 

-  4= 

llX   7  = 

.-.    77- 

-  7 

7x4= 

.-.28- 

_  7= 

77- 

-11 

28- 

-  4= 

11X12  = 

.-.132- 

-12 

8x4  = 

.-.32- 

-  8= 

132- 

-11 

32- 

-  4= 

12  X   4  = 

.-.    48- 

-  4 

9x4= 

.-.36- 

-  9  = 

48- 

-12 

36- 

-  4= 

8x12  = 

.-.    96- 

-12 

6X5  = 

.-.  30- 

-  6  = 

96- 

-  8 

30- 

-  5  = 

9x   4= 

.-.    36- 

-  4 

6x6  = 

.-.36- 

-  6  = 

36- 

-  9 

6x7  = 

.-.42- 

IT  

9x   9= 

.-.    81- 

-  9 

42- 

-  6= 

7X   7= 

.  .    49- 

-  7 

6x8  = 

.-.  48- 

-  8= 

11X11  = 

.-.  121- 

-11 

48- 

-  6= 

12x12= 

.-.  144- 

-12 

6x9= 

.-,54- 

-  9= 

7X12= 

.-.    84- 

-12 

54- 

-  6= 

84-:-    7 

CHAPTER   TWO. 


139 


LESSON    LXVI. 

Name  quotients  at  sight. 

6)30       54       18     J30       <2A      jL8      _72       JL2  ^6  36 

7)j*5       63       14       28       42      _56        77       Jtt  84  ^70 

8)  40       24       48       16       56       96        64        88  32  80 

9)_36      JL8^5_90_27_99_72_64_81  ^08 

Name  quotients  and  remainders  at  sight. 

6)JL9       23J^_39jllJ*7j>7jl6  ^^0 

7)  16       20       25       31        37        40        45        50  55  67 

8)_19       23      J28      _31       ^7      ^3       47       _54  _62  70 


Divide  540  by  6. 


Divide  972  by  9. 


SUGGESTION:    540=54X10            972=900+72. 
6)54x10                                        9)900+72 

726 
707 
728 
972 

9x10=90                                     100+  8=108 
6)180             420             240             480              546 

7)210             350             497             280              847 

8)640              408             320             960              808 

9)450             540             909             918              945 

140  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    LXVIL 

Divide  1792  by  7. 

SUGGESTION:    1792=1400+350+42 
7)1400+850+42 

200+  50+  6=256    Ans. 

1.  At  $7  a  bbl.  for  flour,  how  many  barrels  can  be  bought 
for  $1715? 

2.  If  $1272  is  the  price  paid  for  8  horses,  what  is  the  price 
of  one  horse? 

3.  The  price  paid  for  9  house  lots  was  $9009.     What  was 
the  price  per  lot? 

4.  Four  boys  received  the  same  wages,  which  amounted  in 
6  months  to  $2664.     What  part  of  the  whole  does  each  boy 
receive?     How  many  dollars? 

5.  What  are  the  monthly  wages  of  each  of  the  four  boys? 

6.  How  many  feet  are  there  in  1728  inches? 

7.  How  many  bushels  are  there  in  3600  pecks? 

8.  How  many  dollars  are  there  in  1880  dimes? 

9.  How  many  dimes  are  there  in  1000  cents? 

10.  How  many  feet  are  there  in  2448  inches? 

11.  9  acres  of  land  cost  $3753.     Cost  of  an  acre? 

12.  What  is  |  of  $4949? 

13.  What  is  £  of  8118  miles? 

14.  A  road  468  miles  long  is  divided  into  9  equal  sections. 
What  is  the  length  of  each  section  ? 

15.  What  part  of  the  entire  road  is  one  section  ?  2  sections  ? 

16.  A.  man's  income  during  8  years  was  $17400.     What 
was  his  yearly  income  ? 

17.  A  man  earns  $27000  in  12  years.      What  does  he  earn 
in  1  year? 

18.  At  $121  for  11  barrels  of  flour,  how  much  flour  can  be 
bought  with  $1782? 


CHAPTER  TWO.  141 

LESSON    LXVIII. 

1.  6)$  540           $54             $       5.40  $  _  .54  $6.06 

2.  7)$  630           $63             $       6.30  $  _  .63  $7.70 

3.  8)$  48.16        $  4.88       $       8.72  $     16.24  $  .96 

4.  9)$7218           $  7.29       $     72.18  $  918  $  .81 

5.  6)$  4.86          $48.54        $4800  $4812  $  .12 

$  9.60       $     96.80  $     88.08  $  .08 


7.  9  $1080  $10.80        $       1.08        $6354  $9 


8.  6)$2149  $28.35       $       4.27        $       5.60      $7.91 

9.  457814-^-7=  20.  83762-7-7= 

10.  579486-r-6  =  21.  92352-7-8= 

11.  767856-^8=  22.  526050-7-9= 

12.  324189-7-9=  23.  174968-^.4= 

13.  756648-7-9=  24.  768568-7-8= 

14.  317685-7-5  =  25.  579072-7-6= 

15.  178932-7-6=  26.  607080—5  = 

16.  746856-7-9=  27.  728496-^-6= 

17.  682344-^-4=  28.  259588--7= 

18.  675934-7-7=  29.  960504-r-8= 
.   19.  546752-7-8=  30.  10872549^-9= 


142  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    LXIX. 
1.  Divide  169  by  13. 

169=130+39.  SUGGESTION: 

13)130-(-39  Good  teaching  does  not  leave 

the  learner  to  "guess  work"  ID 
0-f-  3=13  quotient.  his  first  steps  in  division. 

In  the  solution  of  the  examples  of  this  lesson  let  the  necessary 
reduction  be  made  before  the  division  is  performed. 

2.  Divide  196  by  14.  14.  Divide  182  by  13. 

3.  Divide  225  by  15.  15.  Divide  210  by  14. 

4.  Divide  256  by  16.  16.  Divide  240  by  15. 

5.  Divide  289  by  17.  17.  Divide  272  by  16. 

6.  Divide  324  by  18.  18.  Divide  306  by  17. 

7.  Divide  361  by  19.  19.  Divide  342  by  18. 

8.  Divide  400  by  20.  20.  Divide  399  by  19. 

9.  Divide  441  by  21.  21.  Divide  483  by  21. 

10.  Divide  484  by  22.  22.  Divide  528  by  22. 

11.  Divide  529  by  23.  23.  Divide  575  by  23. 

12.  Divide  576  by  24.  24.  Divide  624  by  24. 

13.  Divide  625  by  25.  25.  Divide  700  by  25. 

In  the  following  examples  lead  the  pupil  to  discover  the  answer 
before  performing  the  operations  indicated. 

1.  26x31—13=  11.  64x15—16= 

2.  28x23-r-14=  12.  51xl9-r-17= 

3.  45x22-^-15=  13.  54x25-^-18= 

4.  32x32-~16=  14.  76x18-5-19= 

5.  34x26-r-17=  15.  46x24—23= 

6.  36x45-^-18=  16.  66x18-^-22= 

7.  88x14-5-19=  17.  75x39-^-25  = 

8.  39xl8-r-13=  18.  72x28-r-24= 

9.  42x24-r-14=  19.  95x81-5-19  = 

10.  30xl7-i-15=  20.  72x46-^-18= 


CHAPTER  TWO. 


143 


LESSON    LXX. 


1.  Divide  11271  by  13. 


OPERATION: 

867 


13)11271 
104 

87 

78 

91 

91 


SUGGESTION:  To  aid  the  pupil  in  this 
most  difficult  of  Third  Grade  work,  let  a 
table  of  multiples  of  the  divisor  be  placed 
before  him  as  a  key  to  the  successive  figures 
of  the  answer  sought,  thus: 


13x1=13 
13x2=26 
13x3=39 

13x4=52 
18x5=65 

13x6=78 

13x7=  91 
13x8=104 
13x9=117 

By  inspecting  the  operation  in  the  margin  above,  it  will  be  seen 
that  the  first  division  is  that  of  112  hundreds;  the  second  87  tens; 
the  third  9 1  ones. 

By  the  aid  of  the  key  the  pupil  is  able  to  see  eight  13's  in  112, 
six  13's  in  87,  and  seven  13's  in  91.  Since  the  8  is  eight  hundreds 
(why?),  the  6  six  tens  (why?),  and  the  7  seven  ones  (why?),  each 
figure  is  written  in  its  proper  place  over  the  dividend. 

2.  With  13  for  the  divisor,  tell  at  sight,  with  the  aid  of  the 
key,  the  first  figure  of  the  quotient  in  the  following  dividends. 
Also  write  it  in  its  proper  place  over  the  dividend  : 

358  1948  759  42865 

469  2961  876  115832 

495  4217  9741  103200 

548  5841  10741  105300 

637  6793  77600  90400 

675  8918  79815  92500 


144  FIRST  BOOK  IN  ARITHMETIC. 


LESSON    LXXI. 

1.  Make  a  table  to  serve  as  a  key  to  the  divisor  14,  and  by 
its  aid  tell  at  sight  the  figures  of  the  quotients  in  the  follow- 
ing examples : 

14)106316  14)12306  14)11326" 


83  110  12 


121  126  126 


66 


Test  the  correctness  of  your  answers  by  completing  the  opera- 
tions. 

2.  With  15  for  a  divisor,  tell  at  sight  the  first  quotient  fig- 
ure in  the  following  dividends,  and  write  it  in  its  proper  place 
over  the  dividend. 

2764  4890  6890  10240 

2950  5360  7218  11914 

3348  568  8314  12360 

8785  595  8740  13212 

4360  6340  9618  14800 

3.  With  16  for  a  divisor,  tell  at  sight  the  first  figure  of  the 
quotient  in  the  following  dividends : 

3365  1147  1330  1596 

5021  1518  879  1258 

985  1004  1278  1096 

4.  With  17  for  a  divisor,  tell  at  sight  the  first  quotient  fig- 
ure : 

487  6881  11281  14850 

568  7250  12940  16590 

984  1503  18460  10851 

5.  With  18  for  a  divisor,  tell  at  sight  the  first  quotient  fig- 
ure : 

3540  6280  1208  1618 
4960  1005  1308  1678 
8750  1136  1495  1798 


CHAPTER  TWO. 
LESSON    LXXII. 


145 


13)  491: 

3419 

1131 

1274 

• 

11232 

14)  784 

1218 

10710 

12418 

1372 

15)1275 

1440 

6685 

7020 

9720 

16)  896 

1248 

5536 

10960 

12624 

17)1071 

1479 

7~956  • 

nlol 

14~943 

18)  810 

1368 

8208 

11772 

15768 

19)  912 

1444 

6194 

12844 

15371 

20)  1580 

1960 

6020 

16340 

13560 

21)4410 

8l90 

12768 

16149 

18608 

22)  1936 

9~504 

14454 

17798 

19976 

23)1955 

2254 

6l64 

17687 

21114 

24)1944 

.   2184 

75T2 

16224 

20616 

25)6250 

i2~5b 

19225 

20450 

23~950 

24)21624 

26f6 

14520 

20304 

19080 

19)1824 

11704 

17252 

13775 

5090 

146  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    LXXIII. 

1.  In  1840  eggs  how  many  dozen? 

2.  If  a  i$an,  whose  salary  is  $1500  a  year,  is  paid  each 
month,  what  is  the  monthly  payment? 

3.  How  many  feet  in  3468  inches? 

4.  $5850  was  the  price  paid  for  13  acres  of  land.     What 
was  the  price  per  acre? 

5.  If  $6.66  is  the  price  paid  for  18  Ibs.  of  tea,  what  is  the 
price  per  Ib. ?     What  would  25  Ibs.  cost  at  that  price? 

6.  How  many  days  are  there  in  648  hours  ?    In  3048  hours? 

7.  A  piano  was  sold  for  $540  on  monthly  payments  of  $15. 
How  many  months  did  it  take  to  pay  for  the  piano?    How 
many  years? 

8.  A  lot  of  18  front  feet  sells  for  $3816.    What  is  the  price 
per  front  foot? 

9.  A  lot  of  24  feet  front  sells  for  $11232.     What  is  the 
price  per  foot? 

10.  A  lot,  20  feet  front  by  125  feet  deep,  is   quoted   at 
$4000.     What  is  the  price  per  front  foot? 

11.  At  $48  for  6  ice  boxes,  what  would  25  ice  boxes  cost? 

12.  At  $12  for  5  window  curtains,  what  would  15  window 
curtains  cost? 

13.  Cost  of  |  of  63  heifers  at  $21  each? 

14.  Cost  of  |  of  63  cows  at  $50  a  head? 

15.  The  cost  of  J  of  96  books  is  £  of  $72.     What  is  the 
price  of  the  books  by  the  dozen? 

16.  When  6  acres  of  land  are  worth  $366,  what  are  8  acres 
worth? 

17.  At  $70  for  10  tons  of  coal,  how  many  tons  can  be 
bought  for  $210? 

18.  At  96  cents  for  8  Ibs.  of  beef,  how  many  pounds  will 
$1.32  pay  for? 


CHAPTER  TWO.  147 

LESSON    LXXIV. 

1.  A  score  sometimes  means  20.     How  old  is  a  man  whose 
age  is  three  score  years  and  ten? 

2.  A  boy  had  of  marbles  a  score  and  a  dozen.     How  many 
marbles  had  he? 

3.  24  sheets  of  paper  make  a  quire.     A  boy  had  of  paper  2 
quires  and  a  dozen  sheets.     How  many  sheets  had  he? 

4.  How  many  sheets  in  1  of  a  quire?    \  ?    l?    1?    |?    ^L? 
•  5.  20  quires  of  paper  make  a  ream.     How  many  sheets  of 
paper  in  a  ream?    How  many  sheets  of  paper  in  l  ream? 
1  ream? 

6.  If  paper  is  bought  at  $2.50  a  ream  and  sold  at  a  cent  a 
sheet,  what  is  the  profit  on  one  ream? 

7.  8  is  one  factor  of  32.     What  is  the  other  factor? 

8.  8  is  one  part  of  13.     What  is  the  other  part? 

9.  What  are  the  factors  of  63? 

10.  27  is  one  part  of  63.     What  is  the  other? 

11.  Given  several  numbers  to  find  their  sum. 

12.  Given  the  sum  of  two  numbers  and  one  of  them  to  find 
the  other. 

13.  Given  the  sum  of  several  numbers  and  all  the  numbers 
but  one  to  find  that  one. 

14.  Given  two  numbers  to  find  their  difference. 

15.  Given  minuend  and  subtrahend  to  find  remainder. 

16.  Given  minuend  and  remainder  to  find  subtrahend. 

17.  Given  subtrahend  and  difference  to  find  minuend. 

18.  Given  the  parts  to  find  the  whole. 

19.  Given  the  factors  to  find  their  product. 

20.  Given  two  or  more  numbers  to  find  their  product. 

21.  Given  multiplicand  and  multiplier  to  find  product. 

22.  Given  product  and  multiplicand  to  find  multiplier. 

23.  Given  product  and  multiplier  to  find  multiplicand. 


148  FIRST  BOOK  IN  ARITHMETIC. 

CHAPTER    III. 


LESSON    I. 

ORAL  PROBLEMS. 

1.  I  buy  a  book  for  12c.  and  some  paper  for  8c.     How 
much  change  should  I  receive  if  I  give  the  dealer  25c.  ? 

2.  A  boy  had  15  marbles,  found  9,  and  then  lost  8.     How 
many  had  he  left? 

3.  John  put  36  nuts  into  three  piles;  into  one  14,  into 
another  12.     How  many  were  put  into  the  third  pile? 

4.  Joe  had  50c.  and  paid  out  20c.  for  candy  and  15c.  for  a 
slate.     How  much  did  he  have  left? 

6.  Having  27  marbles,  I  gave  12  to  a  boy  and  lost  5.    How 
many  had  I  left? 

6.  Bought  a  watch  for  f80;  paid  $40  down  and  $20  at 
another  time.     How  much  remained  unpaid? 

7.  A  gentleman  was  paid  $45  for  labor.    How  much  had  he 
left  after  paying  $20  for  cloth,  $9  for  wood,  and  $7  for  flour? 

8.  Bought  a  watch  for  $40,  a  chain  for  $15,  and  a  key  for 
$3.     How  much  is  lost  by  selling  them  for  $50? 

9.  If  a  pole  is  75  feet  high  and  40  feet  are  cut  off  at  one 
time  and  20  feet  at  another,  how  much  is  left? 

10.  A  farmer  put  18  sheep  into  one  pasture,  and  12  into 
another.     How  many  can  he  put  into  the  third  so  that  there 
will  be  45  sheep  in  the  three  pastures? 

11.  By  taking  $1  to  the  grocery,  how  much  may  you  pay 
for  some  tea,  some  cheese,  and  some  oil? 

12.  Buy  some  sugar,  some  coffee  and  some  meat,  and  pay 
75c.  for  all. 

13.  A  suit  costs  $50.     If  the  coat  costs  $30  and  the  vest 
$5,  what  is  the  cost  of  the  pantaloons? 


CHAPTER  THREE.  149 

LESSON     II. 

1.  If  $54  is  paid  a  boy  for  9  weeks  how  much  does  he 
receive  each  week? 

2.  1  square  yard  equals  9  square  feet.     How  many  square 
feet  do  8  square  yards  equal? 

3.  How  many  ounces  do  8  pounds  equal  if  1  pound  equals 
12  ounces? 

4.  Paid  81  cents  for  9  yards  of  ribbon.     What  was  the  price 
per  yard? 

5.  If  7  men  can  build  a  wall  in  12  days  in  what  time  can  1 
man  build  it? 

6.  If  1  man  can  dig  a  trench  in  12  days,  in  what  time  can 
8  men  dig  it? 

7.  A  is  traveling  at  the  rate  of  9  miles  an  hour.     In  what 
time  will  he  complete  a  journey  of  108  miles? 

8.  B  paid  $6  for  a  vest,  and  3  times  as  much  for  a  coat. 
How  much  was  paid  for  both? 

9.  C  rode  9  miles  and  D  9  times  as  far.     How  far  did  they 
both  ride? 

10.  The  distance  from  A  to  B  is  63  miles,  which  is  7  times 
the  distance  to  C.     How  far  is  it  to  C? 

11.  A  tree  is  96  feet  in  height,  which  is  8  times'  the  circum- 
ference at  the  base.     What  is  the  circumference? 

12.  A's  monthly  expenses  are  $96  which  is  12  times  his 
expenses  for  car  fare.     How  much  does  he  pay  for  car  fare? 

13.  A  farmer  sold  6  tons  of  hay  at  $12  a  ton,  and  received 
all  but  $12  in  cash.     How  much  did  he  receive  in  cash? 

14.  A  drover  sold  7  sheep  to  one  man  and  5  to  another. 
At  $9  a  head  how  much  should  he  receive? 

15.  In  what  time  will  a  freight  train  traveling  at  the  rate  of 
12  miles  an  hour  complete  a  distance  of  132  miles? 

16.  If  $63  are  paid  for  7  tons  of  coal,  how  much  should  be 
paid  for  5  tons? 


150  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    III. 

1.  If  3  cords  of  wood  cost  $36,  what  is  the  cost  of  8  cords? 

2.  If  4  men  can  plow  a  field  in  12  days,  in  what  time  can 
6  men  plow  it? 

3.  At  $8  each,  what  is  the  cost  of  2  of  20  cloaks? 

o 

4.  In  how  many  days  can  5  men  reap  a  field  of  grain,  if  3 
men  can  do  it  in  10  days? 

5.  How  many  tons  of  coal  at  $8  a  ton,  may  be  exchanged 
for  4  barrels  of  flour  at  $6  a  barrel? 

6.  If  6  feet  of  street  pavement  cost  $48,  what  is  the  cost 
of  9  feet? 

7.  How  many  men  can  dig  a  trench  in  12  days,  if  8  men 
can  dig  it  in  9  days? 

8.  How  many  weeks  at  $12  a  week,  should  a  man  work  to 
pay  for  8  tons  of  coal  at  $6  a  ton  ? 

9.  What  is  the  cost  of  7  barrels  of  flour,  if  8  barrels  cost 
$56? 

10.  What  is  the  cost  of  riding  12  miles,  if  it  costs  72  cents 
to  ride  8  miles? 

11.  At  what  price  per  barrel  may  6  barrels  of  flour  be  ex- 
changed for  9  chairs  at  $4  each  ? 

12.  If  9  men  can  mow  45  acres  of  grass  in  1  week,  how 
many  acres  can  12  men  mow  in  the  same  time? 

13.  If  9  boxes  of  lemons  are  worth  $54,  how  much  are  7 
boxes  worth? 

14.  How  many  men  in  9  days  can  do  as  much  work  as  12 
men  in  6  days  ? 

15.  If  5  pounds  of  sugar  cost  40  cents,  what  is  the  cost  of 
i  of  a  pound  ? 

16.  What  is  the  cost  of  |  of  14  tons  of  coal  at  $7  a  ton? 

17.  If  8  men  can  earn  $320  in  1  month,  how  much  can  12 
men  earn  in  the  same  time  ? 

18.  If  3  yards  of  cloth  cost  $7,  what  is  the  cost  of  21  yards? 
SUGGESTION:  21  yards  cost  7  times  as  much  as  3  yards. 


CHAPTER  THREE.  151 

LESSON     IV. 

1.  If  a  farmer  feeds  12  tons  of  hay  in  6  weeks,  how  many 
tons  does  he  feed  in  12  weeks? 

2.  How  far  can  a  man  walk  in  j-  of  a  day,  if  he  walks  20 
miles  in  one  day? 

3.  How  many  yards  of  cloth  may  be  bought  for  $7,  if  36 
yards  are  bought  for  $4  ? 

4.  Bruce  rode  8  hours  at  the  rate  of  35  miles  in  5  hours.  • 
How  far  did  he  ride? 

5.  If  9  men  can  dig  36  rods  of  ditch  in  one  day,  in  how 
many  days  can  12  men  dig  it? 

6.  In  how  many  weeks  can  9  men  do  as  much  work  as  6 
men  can  in  12  weeks? 

7.  If  4  men  can  build  a  wall  in  10  days,  how  many  men 
can  build  it  in  8  days? 

8.  If  8  melons  are  worth  24  oranges,  how  many  melons  are 
worth  36  oranges? 

P.  If  5  men  can  paint  a  house  in  12  days,  how  many  men 
can  paint  it  in  1  of  the  time? 

10.  At  8  dimes  a  foot,  what  is  the  cost  of  3  yards  1  foot  of 
iron  railing? 

11.  At  1  cent  a  pound,  what  is  the  cost  of  1  ton  of  hay? 
4  of  a  ton? 

0 

12.  If  8  men  can  do  a  piece  of  work  in  8  days,  in  what  time 
can  8  men  do  a  piece  of  work  twice  as  large? 

13.  How  much  is  gained  if  3  dozen  apples  are  bought  at  8c. 
a  dozen  and  sold  at  Ic.  each? 

14.  Two  men  start  from  the  same  point  and  travel  in  op- 
posite directions,  one  5  miles  an  hour,  the  other  7  miles  an 
hour.     How  far  apart  are  they  in  7  hours? 

Id.  Two  men  start  from  the  same  point  and  travel  in  the 
same  direction,  one  5  miles  an  hcwir,  the  other  12  miles  an 
hour.  How  far  apart  are  they  in  9  hours? 


152  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    V. 

1.  If  10  men  can  build  a  wall  in  30  days,  in  what  time  can 
12  men  build  it? 

2.  If  20  boys  can  build  a  fence  in  4  days,  how  many  boys 
can  build  it  in  10  days? 

3.  How  many  men  in  4  days  can  do  as  much  as  8  men 
can  do  in  40  days? 

4.  If  5  men  can  lay  a  water  pipe  in  20  days,  how  many 
men  can  do  it  in  ^  the  time? 

5.  If  6  men  can  mow  a  field  of  grass  in  8  days,  in  what 
time  can  4  men  mow  \  as  much? 

6.  How  much  is  the  cost  of  -|  of  15  yards  of  silk  if  7  yards 
cost  $21? 

7.  What  is  the  cost  of  f  of  12  tables,  if  8  tables  cost  $72? 

8.  How  many  sheep  can  be  bought  for  $77  if  6  sheep  can 
be  bought  for  $11? 

9.  How'' many  hogs  can  be  bought  for  $60  if  3  hogs  can  be 
bought  for  $10? 

10.  If  6  chairs  cost  f  of  $12  what  is  the  cost  of  12  chairs? 

11.  If  5  caps  cost  $8,  how  many  caps  can  be  bought  for  $56? 

12.  A  earns  A  of  $15  in  4  days.    How  much  does  he  earn  in 
9  days? 

13.  If  12  men  can  reap  a  field  of  grain  in  8  days,  in  what 
time  can  6  men  do  it? 

14.  B  earns  in  5  days  -|  of  $20.     How  much  can  he  earn 
in  12  days? 

15.  If  3  men  can  plow  a  field  in  |  of  12  days,  in  what  time 
can  9  men  plow  it? 

16.  How  many  men  in  12  days  can  do  as  much  as  9  men 
can  in  |  of  12  days? 

17.  If  30  sleds  cost  $45,  what  is  the  cost  of  §  of  9  sleds? 


CHAPTER  THREE.  153 

LESSON     VI. 

1.  If  9  men  can  build  a  wall  in  8  days,  how  many  men  can 
build  it  in  12  days? 

2.  How  many  men  can  cut  a  field  of  grass  in  8  days,  if  12 
men  can  cut  it  in  4  days  ? 

3.  How  many  pounds  of  sugar  at  10  cents  a  pound,  may  be 
exchanged  for  |  of  a  barrel  of  flour  at  $5  a  barrel? 

4.  In  how  many  days  can  6  men  build  a  wall,  if  5  men  can 
do  it  in  12  days? 

5.  What  is  the  cost  of  32  ounces  of  tea  at  $2  a  pound? 

6.  At  $3  a  gallon,  what  is  the  cost  of  36  quarts  of  wine? 

7.  What  is  the  cost  of  -|  of  a  hogshead  of  beer  at  12  cents 
a  gallon? 

8.  At  8  cents  an  hour,  how  much  can  a  boy  earn  in  |  of  a 
day? 

9.  What  is  the  cost  of  painting  27  square  feet  of  floor  at 
12  cents  a  square  yard? 

10.  At  9  cents  a  peck,  what  is  the  cost  of  3  bushels  of 
potatoes  ? 

11.  What  is  the  cost  of  J  of  15  tons  of  coal  at  $8  a  ton? 

o 

12.  If  l  of  a  ton  of  hay  cost  $ 3,  what  is  the  cost  of  6  tons? 

13.  What  is  the  cost  of  20  oranges,  if  8  oranges  cost  40 
cents  ? 

14.  At  f  1  a  pennyweight,  what  is  the  cost  of  a  gold  chain 
that  weighs  3  ounces  ? 

15.  At  8  cents  a  quart,  what  is  the  cost  of  3  gallons  of  oil? 

16.  If  i  of  a  dozen  of  eggs  cost  4  cents,  what  is  the  cost 
of  9  dozen? 

17.  If  i  of  20  oranges  cost  20  cents,  what  is  the  cost  of  1 
dozen? 

18.  If  l  of  24  sheep  cost  $24,  what  is  the  cost  of  1  dozen? 

19.  If  4  apples  cost  10  cents,  what  is  the  cost  of  12  apples? 

20.  What  is  the  cost  of  32  caps,  if  8  caps  cost 


154  FIRST  BOOK  IN  ARITHMETIC. 

LESSON     VII. 

1.  How  many  pounds  of  sugar  at  8  cents  a  pound,  may  be 
exchanged  for  6  dozen  of  eggs  at  12  cents  a  dozen? 

2.  At  $12  a  week,  how  much  can  a  man  earn  in  12  work- 
ing days? 

3.  How  much  can  a  boy  earn  in  |  of  an  hour,  at  1  cent  a 
minute? 

4.  What  is  the  cost  of  riding  |  of  15  miles,  at  the  rate  of 
9  cents  a  mile  ? 

5.  What  is  the  cost  of  riding  12  miles,  at  the  rate  of  |  of 
12  cents  a  mile? 

6.  At  12  cents  a  quart,  what  is  the  cost  of  J  a  peck  of  nuts? 

7.  If  A  can  earn  $3  in  *  of  a  day,  how  much  can  he  earn 
in  9  days  ? 

8.  How  far  can  B  travel  in  12  hours,  if  he  can  travel  4 
miles  in  l  of  an  hour? 

Z 

9.  At  12  cents  a  foot,  what  is  the  cost  of  3  yards  of  flooring? 

10.  What  is  the  cost  of  7  quarts  of  peas,  at  12  cents  a  half- 
peck? 

11.  At  12  cents  a  peck,  what  is  the  cost  of  3  bushels  of  oats? 

12.  What  is  the  cost  of  1  peck  of  beans,  at  8  cents  a  quart? 
13   What  is  the  cost  of  5  yards  of  pavement,  at  $4  a  foot? 

14.  If  5  horses  consume  a  quantity  of  oats  in  12  days,  in 
what  time  can  6  horses  consume  it? 

15.  At  $1  a  cwt.  what  is  the  cost  of  2  tons  of  hay? 

16.  If  the  heart  beats  30  times  in  l  of  a  minute,  how  many 
times  does  it  beat  in  \  of  a  minute? 

o 

17.  If  a  boy  can  travel  J  of  a  distance  in   1  hour,  in  what 
time  can  he  travel  the  distance  and  return? 

18.  If  a  barrel  of  flour  last  a  family  of  7  persons  12  weeks, 
how  long  will  it  last  a  family  of  14  persons  ? 

19.  How  many  yards  of  cloth  can  be  had  for  $18,  if  12 
yards  cost  $36? 


CHAPTER  THREE.  155 

LESSON     VIII. 

1.  Sold  5  yards  of  cloth  for  $30,  thereby  losing  $6.     What 
was  the  cost  per  yard? 

2.  What  is  the  cost  per  pound  if  6  pounds  of  sugar  are  sold 
for  60c.,  thereby  gaining  6c.? 

3.  Bought  4  barrels  of  flour  for  $32  and  sold  it  for  $36. 
What  was  the  gain  per  barrel? 

4.  If  6  quarts  of  oil  cost  60c.  and  are  sold  for  72c.,  how 
much  is  gained  per  quart? 

5.  If  £  of  a  pound  of  rice  cost  8  cents,  what  is  the  cost  of 
5  pounds? 

6.  If  -I  of  a  cord  of  wood  cost  $4,  what  is  the  cost  of  9 

5 

cords  ? 

7.  If  12  pencils  cost  30  cents,  what  is  the  cost  of  2  pencils? 
SUGGESTION:    2  pencils  cost  Ye  as  much  as  12  pencils. 

8.  If    15  oranges  cost  35  cents,  what  is  the   cost   of    3 
oranges  ? 

9.  If  7  tops  cost  12  cents,  what  is  the  cost  of  35  tops? 

10.  What  is  the  cost  of  9  hats,  if  27  hats  cost  $36? 

11.  What  is  the  cost  of  4  pictures,  if  16  pictures  cost  $48? 

12.  If  28  books  cost  $20,  what  is  the  cost  of  7  books? 

13.  What  is  the  cost  of  12  chains,  if  36  chains  cost  $24? 

14.  What  is  the  cost  of  7  head  of  sheep,  if  56  head  cost  $96? 

15.  How  far  does  a  man  walk  in  3  days  if  he  walks  108 
miles  in  27  days? 

16.  B  travels  12  hours  at  the  rate  of  36  miles  in  9  hours. 
How  far  did  he  travel?  * 

17.  How  much  can  C  earn  in  8  days,  if  he  can  earn  $60  in 
40  days? 

18.  If  -|  of  a  ton  cost  $6,  what  is  the  cost  of  9  tons? 

19.  If  6  lemons  are  worth  9  peaches,  how  many  peaches 
are  24  lemons  worth? 


156  FIRST  BOOK  IN  ARITHMETIC, 

LESSON  IX. 

1.  I  of  $24  is  $4  more  than  was  paid  for  a  ton  of  hay. 
How  much  did  it  cost  ? 

2.  $  5  more  than  |  of  $32  was  paid  fora  suit.     How  much 
did  it  cost  ? 

3.  Mr.  A  set  off  for  a  field  4  of  35  acres  and  8  acres  more. 

o 

How  many  acres  were  in  the  field  ? 

4.  |  of  $56  is  $5  less  than  the  cost  of  a  watch.     What  is 
the  cost  of  the  watch  ? 

5.  |  of  $70  is  $10  less  than  the  price  of  my  suit.     What 
is  the  cost  of  my  suit? 

6.  -|  of  81  acres  is  10  acres  more  than  is  in  my  orchard. 
How  many  acres  are  in  the  orchard  ? 

7.  |  of  84  miles  is  10  miles  more  than  B  traveled  yester- 
day.    How  far  did  he  travel  yesterday  ? 

8.  C  gave  $96  for  a  watch  and  ^  as  mucn  less  $9  for  a 
chain.     How  much  was  given  for  the  chain  ? 

9.  D  having  144  cattle  sold  ^  of  them  less  14  cattle.  How 
many  cattle  were  sold  ? 

10.  E  is  63  years  old  and  his  wife  -I  as  old  and  10  years 
more.     How  old  is  the  wife  ? 

11.  A  gentleman  had  $108  in  bank  and  |-  as  much  and  $16 
more  in  his  pocket.     How  much  has  he  in  his  pocket  ? 

12.  §  of  $63  was  paid  for  9  yards  of  silk.     What  is  the 
cost  per  yard  ? 

13.  $  of  $96  was  paid  for  12  barrels  of  flour.     How  much 
was  paid  per  barrel  ? 

14.  If  JL  of  $72  is  paid  for  8  tons  of  coal,  what  is  the  price 
per  ton  ? 

15.  T5-  of  96  years  is  4  times  John's  age.     How  old  is  he  ? 

16.  4  of  $63  is  9  times  the  cost  of  my  hat.     What  is  the 
cost  of  it  ? 


CHAPTER  THREE.  157 

LESSON   X. 

1.  If  l  a  box  of  candy  cost  9  cents,  what  is  *  of  a  box 
worth? 

2.  What  is  the  cost  of  1  of  a  pound  of  butter,  if  -|  a  pound 
cost  12  cents? 

3.  If  i  of  a  pound  of  nuts  cost  8  cents,  what  is  the  cost  of 
1  of  a  pound? 

4.  What  is  J  of  the  distance  from  A  to  B,  if  J  of  the  dis- 

o  ,  o 

tance  is  10  miles? 

5.  If  I-  of  a  field  contains  9  acres,  how  many  acres  does  -J 
of  the  field  contain? 

6.  What  is  -l    of  A's  journey,  if  1  of  the  distance  is  12 
miles? 

7.  If  1  of  B's  age  is  8  years,  what  is  -I  of  his  age? 

8.  What  is  1  of  C's  money,  if  -l  of  it  is  $12? 

9.  If  -1  of  an  acre  of  ground  is  worth  $ 6,  what  is  J  of  an 
acre  worth? 

10.  What  is  1  of  the  height  of  a  tower,  if  -l   of  the  height 
is  12  feet? 

11.  If  i  of  the  width  of  a  street  is  9  feet,  what  is  -l  of  the 
width? 

12.  What  is  J^  of  the  cost  of  a  gentleman's  suit,  if  ^  of  the 
cost  is  $12? 

13.  If  -l  of  a  piece  of  work  can  be  done  in  6  days,  in  what 
time  can  1  of  it  be  done? 

14.  What  is  -^  of  a  trip  to  Salt  Lake,  if  J  of  the  cost  is  $9? 

15.  If  .1.  of  the  cost  of  building  a  wall  is  $4,  what  is  ^ 
of  the  cost? 

16.  What  is  J-2-  of  the  number  of  men  in  a  military  com- 
pany, if  -l  of  the  number  is  8  men? 

17.  If  ^  of  the  cost  of  a  trip  to  San  Francisco  is  $9,  what 
is  -l  of  the  cost? 


158  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XI. 

1.  If  i  of  a  pound  of  coffee  cost  8  cents,  what  is  the  cost 
of  |  of  a  pound?  - 

2.  If  1  of  a  peck  of  apples  cost  9  cents,  what  is  the  cost  of 
|  of  a  pound? 

3.  If  J  of  a  yard  of  cloth  cost  7  cents,  what  is  the  cost  of  | 

O  O 

of  a  yard? 

4.  What  is  the  cost  of  g  of  a  bushel  of  corn,  if  1  of  a 

O  O 

bushel  cost  8  cents? 

5.  How  far  can  a  man  ride  in  |  of  a  day,  if  he  can  ride  9 
miles  in  i  of  a  day? 

6.  What  is  the  cost  of  |  of  a  pound  of  tea,  if  ^  of  a  pound 
cost  9  cents? 

7.  If  1  of  a  man's  monthly  wages  is  $12,  what  are  his 
wages  for  |  of  a  month? 

8.  If  I  of  a  hogshead  of  sugar  is  worth  $8,  how  much  is  | 
of  a  hogshead  worth? 

9.  What  is  the  cost  of  I  of  an  acre,  if  J  'of  an  acre  cost  $12? 

O  O 

10.  If  i  of  A's  age  is  7  years,  what  is  7  of  his  age? 

11.  What  is  |  of  the  distance  from  E  to  F,  if  J,  of  the  dis- 

y  y 

tance  is  12  miles? 

12.  If  ^  of  a  field  contains  8  square  rods,  what  does  T70 
of  a  field  contain? 

13.  What  is  the  area  of  ^  of  a  grass  plat,  if  ^  of  it  is  12 
square  rods? 

14.  If  9  sheep  is  Jj  of  a  certain  flock  of  sheep,  how  many 
are  ^  of  the  flock? 

Id.  What  is  ^  of  the  number  of  trees  in  an  orchard,  if  ^ 
is  12  trees? 

16.  If  ^  of  a  road  can  be  repaired  in  8  days,  in  what  time 
can  a72-  of  it  be  repaired? 


CHAPTER   THREE.  159 

LESSON     XII. 

I.  If  1  of  a  quart  of  molasses  costs  12  cents,  what  is  the 
cost  of  -|  of  a  quart? 

£.  What  is  the  cost  of  |  of  a  pound  of  butter,  if  1  of  a 
pound  cost  8  cents? 

3.  If  1  of  a  dozen  of  oranges  cost  8  cents,  what  is  the 
cost  of  I  of  a  dozen  ? 

o 

4.  What  is  -I  of  the  height  of  a  a  house,  if  l  of  the  height 
is  9  feet? 

5.  If  1  of  a  field  of  grass  is  worth  $8,  what  is  the  value  of 
I  of  it? 

o 

6.  What  is  |  of  C's  age,  if  |  of  his  age  is  12  years? 

7.  If  i   of  a  grocer's  sales  for  one  day  is  $8,  what  is  | 
of  the  sales? 

8.  What  is  |  of  my  money  if  1  of  it  is  $12?  ' 

9.  If  1  of  a  quantity  of  linen  costs  $9,  what  is  the  cost  of 
|  of  it?' 

10.  What  is  ^  of  the  cost  of  a  watch,  if  |  of  the  cost  is  $12? 

II.  If  l  of  a  crate  of  lemons  is  worth  $9,  what  is  |  of  the 
crate  worth? 

12.  What  is  j5L.  of  the  value  of  a  quantity  of  wheat,  if  1 
of  the  quantity  is  worth  $12? 

13.  If  -l  of  the  cost  of  a  suit  of  clothes  is  $4,  how  much  is 
|  of  the  cost? 

O 

14.  What  is  ^  of  B's  farm  if  1  of  the  farm  is  8  acres? 

15.  If  -^  .of  a  sale  of  flour  yields  $7,  what  is  the  yield  of  | 
of  the  sale? 

16.  What  is  J-  of  the  height  of  a  flag  staff,  if  JL  of  the 
height  is  12  feet? 

17 '  ^  iV  °^  J°hn's  weight  is  6  pounds,  what  is  |  of  his 
weight  ? 


160  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XIII. 

1.  How  far  can  A  travel  in  |  of  a  day,  if  he  can  travel  9 
miles  in  i  of  a  day? 

2.  If  a  boy  can  earn  12c.  in  -J   of  an  hour,  how  much  can 
he  earn  in  |  of  an  hour? 

3.  How  much  greater  is  |  of  36  miles  than  |  of  it? 

4.  If  a  man  can  earn  $60  a  mo&th,  how  much  more  can  he 
earn  in  |  than  in  ^  of  a  month  ? 

5.  If  a  boat  sails  60  miles  in  5  hours,  how  far  does  it  sail  in 
|  of  an  hour? 

6.  How  far  does  a  train  move  in  12  minutes  at  the  rate  of 
60  miles  an  hour? 

7.  If  a  man  earns  $108  in  9  weeks,  how  much  does  he  earn 
each  working  day? 

8.  If  1  of  an  acre  yield  9  bushels  of  wheat,  what  is  the 
yield  of  |  of  an  acre? 

9.  |  of  24  miles  is  J  of  the  distance  from  A  to  B.     How 

o  o 

far  is  it  from  A.  to  B  ? 

10.  3  of  a  man's  age,  which  is  28  years,  is  3  times  the  age 
of  his  son.     How  old  is  the  son? 

77.  3  of  $21  is  i   of  the  cost  of  a  suit  of  clothes.     What 
is  the  cost  of  the  suit? 

12.  g  of  $40  is  5  times  the  cost  of  my  hat.     What  is  the 

o  * 

cost  of  the  hat? 

13.  |  of  a  hogshead  of  wine  is  7  times  what  A  bought. 
How  much  did  he  buy? 

14.  ^7-  of  108  years  is  9  times  John's  age.     How  old  is  he? 

15.  |  of    $54  is  J  of   B's  money.      How  much  money 
has  he? 

16.  ^  of  an  hour  is  5  times  how  many  minutes? 


CHAPTER  THREE.  161 

LESSON    IVX. 

ORAL    PROBLEMS. 

SEE  TABLE  OF  U.  S.  MONEY. 

1.  4  cents  5  mills  equal  how  many  mills?    8  cents  7  mills? 

2.  36  mills  equal  how  many  cents?     58  mills?     79  mills? 

3.  J.  of  48  mills  equals  how  many  cents?     |  of  60  mills? 

4.  5  dimes  7  cents  equal  how  many  cents?     12  dimes  5 
cents? 

5.  28  cents  equal  how  many  dimes?     47  cents?    84  cents? 

6.  1  of  40  cents  equals  how  many  mills?     l  of  24  cents? 

7.  -1  of  45  cents  equals  how  many  mills?     |  of  40  cents? 

8.  8  mills  is  what  part  of  4  cents?     5  mills?     4  mills? 

9.  5  cents  is  what  part  of  4  dimes?     8  cents?     4  cents? 

10.  $3  and  4  dimes  equal  how  many  dimes?     $9  and  7 
dimes  ? 

11.  35  dimes  equal  how  many  dollars?    66  dimes? 

12.  -I  of  4  dimes  is  how  much  greater  than  12  cents? 

o 

13.  12  cents  is  -*-  of  how  many  dimes?    -l  of  how  many 
dimes  ? 

14.  60  dimes  equal  5  times  how  many  cents?    6  times? 

15.  1.  of  a  dollar  is  how  much  greater  than  4  dimes? 

16.  l.  of  a  dollar  is  how  much  greater  than  1  of  a  dollar? 

17.  |  of  a  dollar  equals  how  many  dimes?    How  many 
cents? 

18.  |  of  a  dollar  is  how  much  greater  than  l  of  a  dollar? 

19.  |  of   a  dollar  equal  how  many  cents?      How  many 
dimes? 

20.  8  mills  is  what  part  of  7  cents  2  mills?     9  cents  6  mills? 

21.  12  cents  is  what  part  of  4  dimes  8  cents?     8  dimes  4 
cents  ? 

22.  $5  and  4  dimes  equal  how  many  dimes?     $9  and  5 
dimes? 


162  FIRST  BOOK  IN  ARITHMETIC.- 

LESSON    XV. 
SEE  TABLE  OF  LONG  MEASURE. 

1.  9  feet  6  inches  equal  how  many  inches?     12  feet  8 
inches? 

2.  135  inches  equal  how  many  feet?     159  inches? 

3.  |  of  a  foot  equals  how  .many  inches?    |-  of  a  foot? 

4.  2  rods  equal  how  many  yards?     4  rods? 

5.  2  rods  equal  how  many  feet?    3  rods? 

6.  1-  of  3  feet  equals  how  many  inches?    -i  of  5  feet? 

7.  |  of  a  mile  equals  how  many  rods?    -|  of  a  mile? 

8.  |  of  a  mile  equals  how  many  rods?     |-  of  a  mile? 

9.  5  inches  is  what  part  of  a  foot?     9  inches? 

10.  3  feet  is  what  part  of  2  yards?     5  yards? 

11.  9  inches  is  what  part  of  3  feet?     12  inches? 

12.  3-  of  1  yard  equals  how  many  inches?     *  of  2  yards? 

13.  f-  of  a  mile  is  how  much  greater  than  100  rods? 

o 

14.  How  much  less  is  20  feet  than  12  yards? 

15.  How  much  greater  is  75  inches  than  6  feet? 

16.  80  rods  is  what  part  of  a  mile?     64  rods? 

17.  What  is  the  cost  of  fencing '|  of  a  mile  at  $2  a  rod? 

18.  |  of  a  foot  equals  1-  of  how  many  inches? 

19.  |  of  a  foot  equals  1  of  how  many  yards? 

20.  1  of  a  mile  equals  *  of  how  many  rods? 

21.  1  rod  equals  how  many  half -yards?     3  rods? 

22.  1  yard  equals  how  many  half -feet?     Third-feet? 

23.  12  half -feet  equal  how  many  yards?     24  third-feet? 

24.  9  inches  equal  -I  of  how  many  feet? 

25.  9  feet  equal  l  of  how  many  yards? 

26.  1  mile  equals  8  times  how  many  rods? 


CHAPTER  THREE.  163 

LESSON    XVT. 
SEE  TABLE  OF  DRY  MEASURE. 

1.  5  quarts  1  pint  equal  how  many  pints  ?   9  quarts  1  pint? 

2.  3  pints  equals  what  part  of  6  quarts  ?     Of  9  quarts  ? 

3.  4  pints  equal  \  of  how  many  quarts  ?     J  ?     -J  ? 

4.  7  pecks  5  quarts  equal  how  many  quarts  ?     9  pecks  6 
quarts  ? 

5.  3  quarts  equal  what  part  of  1  peck?     4 quarts? 

6.  5  quarts  equal  |  of  how  many  pecks?     9  quarts? 

7.  1  peck  equals  what  part  of  32  quarts?    48  quarts? 

8.  3  pecks  equal  6  times  how  many  quarts?     6  pecks? 

9.  70  quarts  equal  how  many  pecks?     100  quarts? 

10.  8  bushels  3  pecks  equal  how  many  pecks  ? 

11.  39  pecks  equal  how  many  bushels ?     50  pecks? 

12.  6  pecks  equal  what  part  of  3  bushels?     Of  9  bushels? 

13.  9  pecks  equal  \-  of  how  many  bushels?     12  pecks? 

14.  3  bushels  equal  12  times  how  many  quarts? 

15.  Since  1  bushel  of  wheat  weighs   60   pounds,  ^  of  a 
bushel  weighs  how  many  pounds  ?    f  ? 

16.  5  bushels  equal  how  many  pounds  ?     10  bushels  ? 

17.  10  pounds  equals  what  part  of  a  bushel?     30  pounds? 

18.  What  is  the  cost  of  1  bushel  of  wheat  at  2  c.  a  pound  ? 

19.  What  is  the  weight  of  2  pecks  of  wheat?    3  pecks? 

20.  What  is  the  weight  of  1  bushel  2  pecks  of  wheat  ? 

21.  6  bushels  equal  8  times  how  many  pecks  ? 

22.  12  pecks  equal  \  of  how  many  bushels  ?    -J-?     J? 

23.  12  quarts  equal  \  of  how  many  pecks?     J?      \  ? 

£4.  48  pecks  equal  6  times  how  many  bushels?     12  times? 
25.  I  peck  equals  how  many  pints?    3  pecks? 


164  FIRST  BOOR  IN  ARITHMETIC. 

LESSON    XVII. 

SEE  TABLE  or  AVOIKDUPOIS  WEIGHT. 

1.  2  pounds  8  ounces  equal  how  many  ounces  ?   5  pounds 
10  ounces? 

2.  How  many  pounds  equal  48  ounces  ?    70  ounces  ? 

3.  \  of  a  pound  equals  how  many  ounces  ?    \  of  a  pound  ? 

4.  |  of  a  pound  equals  how  many  ounces  ?    -J  of  a  pound  ? 

5.  |  of  a  pound  equals  how  many  ounces  ?     f  of  a  pound  ? 
£.  How  much  greater  is  3  pounds  than  36  ounces  ? 

7.  3  cwt.  equals  how  many  pounds  ?     5  cwt.  ?     12  cwt.  ? 

8.  -^  cwt.  equals  how  many  pounds  ?    \  cwt.  ?     -|  cwt.  ? 
•     P.  |^  cwt.  equals  how  many  pounds  ?    J  cwt.  ?    •§-  cwt.  ? 

10.  What  part  of  a  pound  is  8  ounces?     12  ounces? 

11.  What  part  of  2  pounds  is  4  ounces?     8  ounces? 

12.  2  tons  equal  how  many  cwt.  ?     4  tons  ?     5  tons  ? 
75.  -|  ton  equals  how  many  cwt.  ?    \  ton  ?    -J  ton  ? 

14.  |-  ton  equals  how  many  cwt.  ?    f  ton  ?     |  ton  ? 

15.  What  part  of  a  cwt.  is  10  pounds  ?     20  pounds  ? 

26.  What  part  of  a  cwt.  is  25  pounds  ?     30  pounds  ? 

27.  How  many  pounds  less  is  15  cwt.  than  1  ton? 
18.  How  much  greater  is  1  cwt.  than  75  pounds  ? 

jf P.  9  ounces  is  what  part  of  1  pound  ?    Of  2  pounds  ? 
20.  2  tons  equals  how  many  cwt.  ?    How  many  pounds  ? 
£1.  j  of  a  ton  equals  how  many  pounds?    -J-  of  a  ton? 
££.  f  of  a  ton  equals  how  many  pounds  ?    f  of  a  ton  ? 
23.  How  much  greater  is  f  of  a  ton  than  9  cwt.  ? 
£2.  8  ounces  equal  \  of  how  many  pounds?    12  ounces? 

25.  60  pounds  equal  \  of  how  many  cwt.  ?     40  pounds? 

26.  12  cwt.  equal  J  of  how  many  tons  ?    8  cwt.  ? 


CHAPTER  THREE.  165 

LESSON    XVIII. 

SEE  TABLE   OF  TIME. 

1.  -1  of  a  minute  equals  how  many  seconds?    -|? 

2.  How  many  minutes  equal  i-  of  an  hour?     |  ? 

3.  What  part  of  an  hour  are  20  minutes?     80  minutes? 

4.  10  minutes  equal  -^  of  how  many  hours? 

5.  |  of  an  hour  is  how  much  greater  than  30  minutes? 

6.  5  hours  30  minutes  equal  how  many  minutes? 

7.  |  of  a  day  is  how  much  greater  than  |  of  a  day? 

8.  2  days  2  hours  equal  how  many  hours? 

9.  39  days  equal  how  many  weeks?     84  days? 

10.  9  weeks  5  days  equal  how  many  days? 

11.  |-  of  a  year  is  how  much  less  than  1  year  6  months? 

12.  7  months  is  what  part  of  5  years  and  3  months? 

13.  12  hours  equal  1  of  how  many  days? 

14.  2  days  equal  8  times  how  many  hours? 

15.  How  many  days,  omitting  Sundays,  equal  12  weeks? 

16.  |  of  a  day  is  how  much  greater  than  i  of  a  day? 

17.  9  months  equal  what  part  of  3  years?     9  years? 

18.  8  months  equal  1  of  how  many  years? 

19.  1  of  a  century  equals  how  many  years? 

20.  .|  of  a  century  is  how  much  greater  than  50  years? 

21.  |  of  a  century  is  how  much  less  than  50  years? 

22.  56  months  equal  how  many  years?     79  months? 

23.  59  days  equal  how  many  weeks?     89  days? 

24.  3  weeks  is  how  much  less  than  30  days? 

25.  9  years  is  8  months  greater  than  how  many  months? 

26.  8  weeks  is  6  days  less  than  how  many  days? 


16er  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XIX. 

SEE  TABLE  OF  LIQUID  MEASUKE. 

1.  8  pints  3  gills  equal  how  £aany  gills?     12  pints  2  gills? 

2.  47  gills  equal  how  many  pints?     50  gills? 

3.  1  of  a  pint  equals  how  many  gills?     -|  of  a  pint? 

4.  8  quarts  1  pint  equal  how  many  pints?     12  quarts? 

5.  *  of  6  quarts  equals  how  many  pints?     Of  9  quarts? 

6.  i  of  10  pints  equals  how  many  gills?     Of  12  pints? 

7.  How  much  less  is  1  of  12  pints  than  3  quarts? 

8.  6  gallons  3  quarts  equal  how  many  quarts?     12  gallons? 

9.  80  quarts  equal  how  many  gallons?    1  of  48  quarts? 

10.  What  part  of  3  gallons  is  3  quarts?     Of  6  gallons? 

11.  -i  of  a  hogshead  equals  how  many  gallons?    |? 

12.  4  of  a  hogshead  is  how  much  greater  than  25  gallons? 

13.  |.  of  a  hogshead  is  how  much  less  than  £  of  a  hogs- 
head? 

14.  1  hogshead  equals  how  many  barrels?     |  of   a  hogs- 
head? 

15.  4  hogsheads  equal  how  many  barrels?     10  hogsheads? 

16.  How  much  greater  is  4  hogsheads  than  7  barrels? 

17.  5  quarts  equal  what  part  of  5  gallons?     Of  10  gallons? 

18.  1  gallons  equal  what  part  of  1  hogshead?     9  gallons? 

19.  12  gallons  equal  what  part  of  4.  of  a  hogshead? 

20.  5  gallons  equal  what  part  of  -|  of  a  hogshead? 

21.  39  quarts  equal  how  many  gallons?     47  quarts? 

22.  How  much  greater  is  |  of  a  hogshead  than  48  quarts? 

23.  4  quarts  equal  1  of  how  many  gallons? 

24.  21  gallons  equal  J  of  how  many  hogsheads? 

25.  12  gallons  equal  6  times  how  many  quarts? 


CHAPTER  THREE.  167 

LESSON    XX. 

SEE  TABLE  OF  TBOY  WEIGHT. 

1.  9  pounds  4  ounces  equal  how  many  ounces? 

2.  150  ounces  equal  how  many  pounds?     100  ounces? 

3.  9  ounces  equal  what  part  of  3  pounds?     Of  6  pounds? 

4.  6  ounces  equal  *  of  how  many  pounds?     ^? 

5.  4  ounces   10  pennyweights  equal  how  many  penny- 
weights? 

6.  70  pennyweights  equal  how  many  ounces?    90  pwt.? 

7.  1  of  3  ounces  equal  how  many  pennyweights? 

8.  i  of  3  pounds  equal  how  many  ounces? 

9.  -|  of  2  pounds  equal  how  many  ounces? 

10.  12  pennyweights  equal  1  of  how  many  ounces? 

11.  -|  of  a  pennyweight  equal  how  many  grains? 

12.  |  of  a  pennyweight  is  how  much  greater  than  12  grains? 

13.  12  pennyweights  equal  what  part  of  3  ounces? 

14.  10  pennyweights  equal  |  of  how  many  ounces? 

15.  12  grains  equal  what  part  of  3  pennyweights? 

16.  8  grains  equal  1  of  how  many  pennyweights? 

17.  12  grains  equal  1  of  how  many  pennyweights? 

18.  240  grains  equal  how  many  pennyweights? 

19.  1  gold  dollar  weighs  1  pwt.     What  is  the  value  of  gold 
dollars  that  weigh  1  of  an  ounce? 

20.  What  is  the  value  of  gold  dollars  that  weigh  1  pound? 

21.  What  is  the  value  of  gold  dollars  that  weigh  l  of  a 
pound? 

22.  At  $  1  a  pwt.  what  is  the  value  of  a  gold  chain  that 
weighs  2  ounces? 

23.  1  silver  dollar  weighs  1  oz.     What  is  the  value  of  sil- 
ver dollars  that  weigh  i  pound? 

24.  What  is  the  value  of  silver  dollars  weighing  5  pounds? 


168  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XXL 


NOTATION 

AND   NUMERATION.* 

Bead: 

1. 

2. 

3. 

$100.01 

$1000.10 

$     200200.20 

$500.05 

$1500.05 

$     117803.19 

$900.09 

$2050.05 

$  2002020.02 

$404.40 

$4004.40 

$  5380409.75 

$180.18 

$6600.60 

$  8716580.90 

$227,105 

$7017.71 

$     745400.08 

$808.088 

$8800.08 

$       27685.14 

$650.501 

$9500. 

$25025025. 

$770.07 

$4872.16 

$  6006006. 

$707.70 

$5055.005 

$60060060. 

Bead: 

1.  180  mi.,  45  rds.,  12  ft.,  6  in. 

2.  14  mi.,  27  rds.,  4£  yds.,  3f  ft.,  5  in. 

3.  120  A.,  40  sq.  rds.,  20£  sq.  yds.,  6  sq.  ft. 

4.  14  sq.  rds.,  15  sq.  yds.,  3  sq.  ft.,  120  sq.  in. 

5.  5  sq.  mi.,  40  A.,  40  sq.  rds. 

6.  20  cu.  ft.,  144  cu.  in. 

7.  13  cu.  yds.,  18  cu.  ft.,  25  cu.  in. 

8.  4  gals.,  3  qts.,  2  pts. 

9.  10  bu.,  3  pks.,  5  qts.,  1  pt. 

10.  17  T.,  14  cwt.,  25  Ibs.,  8  oz. 

11.  100  yr.,  200  da.,  4  hr. 

12.  5  wk.,  6  da.,  5  hr.,  40  min.,  20  sec. 

13.  A.  D.  1865,  A.  D.  1885. 

14.  A.  D.  Sept.  1,  1885,  9  o'clock  A.  M.,  12  o'clock. 

15.  Borne  was  founded  753  B.  C. 

16.  Carthage  was  destroyed  B.  C.  146. 


*See  Lessons  XXIV  and  XXV,  Chap.  II. 


CHAPTER  THREE.  169 

LESSON     XXII. 

Group  the  following  into  periods  and  read  : 
SUGGESTION:  In  grouping  into  periods  do  not  use  the  comma. 

1.  1  000  090                 2.  100  000  000  3.  11  175  846 

1  001  001  125  000  125  414  570  184 

1  010  010  400  000  400  29  408  509 

1  100  100  404  404  000  216  457  579 

10  010  010  20  020  020  49  049  049 

10100001  16160106  180108118 

10  900  909  100  100  100  410  415  000 

90  900  009  100  010  001  27  028  029 

25  450  465  107  017  170  14  014  014 

19  190  109  40  400  004  140  114  104 

Write,   grouping  into  periods;   then  read  from  slate   or 
blackboard : 

1.  5  thousand,  five. 

2.  50  thousand,  five. 

3.  500  thousand,  5  hundred. 

4.  548  thousand,  twenty-five. 

5.  1  million,  1  thousand,  one. 

6.  10  million,  10  thousand,  ten. 

7.  25  million,  25  thousand,  25. 

8.  100  million,  100  thousand,  100. 

9.  17  million,  7  thousand,  170. 

10.  808  million,  80  thousand,  8. 

11.  175  million,  190  thousand,  200. 

12.  1  billion,  100  million,  100  thousand. 

13.  1  billion,    19  million,    17  thousand,  7. 

14.  1  billion,  506  million,  560  thousand,  500. 

15.  Eighteen  hundred,  eighty-five. 

16.  Ten  hundred  thousand. 

17.  A  thousand  millions. 


170  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XXIII. 

ADDITION. 

Addition  in  Arithmetic  is  the  name  of  an  operation  by 
which  two  or  more  numbers  of  the  same  kind  are  united  into 
one  equivalent  number  called  the  Sum  or  Amount. 

1.  What  is  the  sum  of  748  Ibs.,  496  Ibs.,  324  Ibs.,  657  Ibs. 
and590lbs.? 

2.  What  is  the  sum  of  1840  mi.,  1492  mi.,  1620  mi.,  2240 
mi.  and  968  mi. 

3.  What  is  the  sum  of  $9628,   $786,  $791,  $9927  and 
$684? 

4.  What  is  the  sum  in  days  of  8  years  of  365  days,  and  1 
year  of  366  days? 

5.  What  is  the  aggregate  weight  of  3  bu.  barley,  48  Ibs. 
each;  3  bu.  corn,  52  Ibs.  each;  3  bu.  corn  meal,  48  Ibs.  each; 

3  bu.  wheat,  60  Ibs.  each? 

6.  What  is  the  aggregate  weight  of  3  bbls.  flour,  196  Ibs. 
each;  2  bbls.  salt,  280  Ibs.  each? 

7.  What  is  the  sum  in  hours  of  4  weeks  of  7  days  each? 

4  working  weeks  of  6  days  each?  4  school  weeks  of  5  days  each? 

8.  How  many  days  are  there  from  the  26th  of  June  to  the 
1st  of  September  inclusive? 

9.  What  is  the  sum  of  $18.49,  $9.075,  $36.47,  $7.098  and 
$67.875? 

10.  What  is  the  sum  of  98,  4640,  396,  7859  and  87? 

11.  How  many  days  are  there  from  September  1  to  June  30 
inclusive? 

12  Five  men  enter  into  business  together.  A  furnishes 
$8770,  B  $5875,  C  as  much  as  A[and  B  less  $1500,  D  as 
much  as  B  and  C,  E  as  much  as  A  and  D .  What  is  their 
united  capital? 


CHAPTER  THREE. 


171 


LESSON  XXIV. 


For  proof  of  accuracy,  see  Lesson  XXXII  Chapter  II. 


1. 

2. 

3. 

4. 

68046 

13222 

74564 

217345 

46258 

12313 

27892 

166459 

86048 

31359 

83571 

225224 

05137 

22441 

13456 

306892 

47346 

14321 

35683 

102755 

99008 

22720 

30907 

214653 

28944 

36642 

65586 

157672 

5. 

6. 

7. 

8. 

15038 

26881 

41919 

93808 

7404 

39665 

19577 

41371 

34971 

33249 

74736 

110525 

30359 

6318 

66768 

102936 

6293 

4318 

7193 

17087 

2875 

34705 

51365 

13251 

64934 

80597 

155497 

220619 

16147 

29997 

52839 

86160 

9. 

10. 

11. 

12. 

80901 

95299 

183134 

225255 

7444 

53806 

16845 

68940 

57068 

18647 

35902 

176974 

17255 

41609 

82182 

86590 

32543 

35077 

75153 

149162 

56063 

46880 

132935 

109355 

33860 

41842 

82939 

283910 

17548 

26876 

44424 

72908 

38556 

44305 

83271 

119557 

39058 

39744 

78861 

117787 

172  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XXV. 

1.  Bought  flour  for  $8796,  coal  for  $9875,  hardware  for 
$25675  and  agricultural  implements  for  $19568.     Sold  the 
flour  at  a  profit  of  $786,  the  coal  at  a  profit  of  $975,  the 
hardware  at  a  profit  of  $5780  and  the  agricultural  implements 
at  cost.     What  were  the  total  receipts? 

2.  Bought  grain  for  $7475,  and  sold  it  at  an  advance  of 
$496;     groceries  for   $5789,   and   sold   at   an   advance    of 
$578.90;  other  merchandise  for  $4850,  and  sold  at  an  advance 
of  -J  the  cost.     What  was  the  amount  of  sales? 

3.  A  fifty  foot  lot  was  purchased  at  $50  a  foot.  Two  houses 
were  erected  thereon  at  a  cost  of  $5068  each.     The  property 
was  sold  at  an  advance  of  $3875  on  the  cost.     What  was  the 
selling  price? 

4.  A  has  $938  which  is  £  of  B's  money.     C  has  as  much 
as  A  and  B.     How  many  dollars  have  A,  B  and  C  together? 

5.  A  farmer  hought  a  farm  paying  $2375  down.     After 
making  two  more  payments  of   $1096  and   $1260  he  still 
owed  $896.     What  was  the  price  of  the  farm? 

6.  Six  loads  of  hay  weigh  as  follows:  3648  Ibs.,  1949  Ibs., 
2783  Ibs.,  2548  Ibs.,  3140  Ibs.  and  2987  Ibs.     What  is  the 
entire  weight  of  the  six  loads? 

7.  A  man  had  $3640.     By  trading  in  live  stock  he  added 
to  his  capital  $1575.     How  much  more  will  enable  him  to 
pay  for  a  farm  worth  $10000? 

8.  The  distance  from  Chicago  to  Appleton,  Wis.,  is  185 
miles;  from   Chicago   to   Ashland,    on   Lake   Superior,    483 
miles;  from  Chicago  to  Devil's  Lake,  173  miles;  from  Chi- 
cago to  Escanaba,  Mich.,   357  miles;  from  Chicago  to  Lake 
Madison,  Minn.,  421  miles.     How  many  miles  would  a  Chi- 
cago traveling  agent  ride  in  visiting  all  these  places,  return- 
ing to  Chicago  from  each  point? 


CHAPTER  THREE.  173 

LESSON    XXVI. 

The  columns  of  figures  in  this  lesson  represent  the  cost  of 
fuel  for  the  schools  of  Chicago  for  the  year  1883-1884.  What 
was  the  total  cost? 

1.  2.  3.  4. 

$143.50  $418.11  $633.98  $782.55 

1174.63  770.64  623.  478.76 

909.12  546.34  377.56  213.20 

584.08  1017.55  971.21  705.79 
602.45  849.34  638.62  978.77 
474.34  753  88  546.53  634.92 
891.38  712.99  601.82  690,05 

487.41  939.38  591.85  589.15 

5.  6.  7.  8. 

$611.89  $530.81  $530.81  $655.03 

272.86  670.88  726.45  1067.89 

628.42  670.06  772.59  709.53 
517.41  434.21  1115.59  872.72 

530.09  703.31  692.55  701.55 
655.44  521.69  478.42  972.02 
807.38  540.  592.42  682.57 

2134.69  684.89  487.73  845.03 

9.  Grain  was   sold  as  follows:       9860   bu.    of  wheat  for 
$3286.33;  8756  bu.  of  corn  for  $4378;  12845  bu.  oats  for 
$4281.67;  1896  bu.  of  rye  for  $932;  786  bu.  of  barley  for 
$393.     How  many  bu.  of  grain  were  sold  and  for  how  much? 

10.  The  heights  of  10  mountain  peaks  in  North  America  are 
given  in  feet  as  follows:      17900,  16000,  15500,  14898,  14,- 
447,  14444,  14271,  14147,  13570  and  11225.     What  would  be 
the  length  of  a  line  that  would  measure  the  united  heights  of 
these  mountains. 


174  FIRST  BOOK  IN  ARITHMETIC. 

LESSON  XXVII. 

The  columns  in  this  lesson  contain  the  number  of  pupils 
enrolled  in  the  Chicago  schools  during  the  year  1883-84. 
What  was  the  total  enrollment? 

1.  2.  3.  4. 

305  1675  1409  1.522 

479  460  1216  1001 

751  1746  2452  654 

1508  1504  900  1156 

728  1057  1130  225 

2177  1750  1499  1641 

1160  1737  1238  1025 

1042  1085 

5.  6.  7.  8. 

1429  1004  1593  1791 

224  1051  488  1472 

1360  1150  1463  1314 

1056  1001  1966  197 

1050  1173  698  1791 

1516  1276  1110  1343 

1336  1287  1221  1726 

1981  1225  139 

9.  How  many  men  in  an  army  consisting  of  52714  infantry, 
5110  cavalry,  6250  dragoons,  3927  light-horse,  928  artillery, 
250  sappers,  and  406  miners? 

10.  Five  persons  deposited  money  in  the  same  bank;  the 
first,   $5897;    the  second,   $12980;  the  third,  $65973;   the 
fourth,  $37345,  and  the  fifth  as  much  as  the  first  and  second 
together;  how  many  dollars  did  they  all  deposit. 

11.  A  has  $3648,  B  has  $7035,  C  has  $429  more  than  A 
and  B  together,  and  D  has  as  much  as  all  the  rest.     How 
many  dollars  has  D?    How  many  have  all? 


CHAPTER  THREE. 

LESSON    XXVIII. 

1.  Find  the  sum  of  \  of  360  days,  f  of  180  days,  |-  of  300 
days,  and  |  of  720  days? 

2.  There  are  63  gallons  in  a  hogshead.     Find  the  sum  in 
gallons  of  }  +  f  +  f  +  -f  +  f  +  -f  of  a  hogshead. 

5.  Find  the  sum  in  rods  of  4  +  4  H- 1  of  a  mile. 

o  o  o 

4.  There  are  144  square  inches  in  a  square  foot.     What  is 
the  sum  in  square  inches  of  -|  and  |-  of  a  square  foot? 

5.  What  is  the  sumx>f  |,  |  and  f  of  a  sq.  ft.,  expressed  in 
square  inches? 

6.  What  is  the  sum  in  seconds  of  J,  £  and  |  of  an  hour? 

7.  What  is  the  sum  of  f  and  f  of  $630.49? 

8.  What  is  the  sum  in  pounds  of  y1^,  /Q,  y70  and  y90  of  a 
ton? 

8.  What  is  the  sum  of  ^y,  T5T,  T7T  and  T9T  of  12  times  $22? 

10.  There  are  12x12x12  cubic  inches  in  a  cubic  foot. 
What  is  the  sum  in  cubic  inches  of  y5^,  j%  and  |^  of  a  cubic 
foot? 

11.  What  is  the  sum  of  y  of  42  gallons,  f  of  45  gallons, 
and  |  of  40  gallons  of  oil? 

12.  What  is  the  sum  of  \\  of  144  sq.  in.,  f  of  144  sq.  in., 
and  I  of  144  sq.  in.? 

13.  What  is  the  sum  of  f  of  $21.56,  |  of  $28.14,  f  of 
$84.21,  and  f  of  $140? 

14.  Some  damaged  goods  that  cost  $1200  sold  for  |  of  the 
cost.     What  did  they  bring? 

Id.  Flour  that  cost  $480  sold  at  an  advance  of  f  of  the 
cost.  What  did  the  flour  sell  for? 

16.  A's  age  is  27  years.  B's  age  is  A's  age  increased  by  | 
of  A's  age.  What  is  B:s  age? 


176 


FIRST  BOOK  IN  ARITHMETIC. 


LESSON    XXIX. 


52    53     54     55       56 

1 

2375 

43281 

6734575 

3456786 

786543489 

321 

2 

3674 

75839 

4659768 

7684538 

875769823 

3 

4789 

83672 

5783684 

8759687 

757364568 

33 

47 

4 

4637 

64368 

5864839 

8475973 

576743689 

i  .* 

5 

8483 

59873 

4579395 

6897528 

846598554 

*  34 

6 

7534 

74358 

8977878 

7958785 

946758765 

48 

7 

5987 

66946 

5766964 

5387649 

597595389 

35 

8 

7638 

77585 

8454346 

7523463 

834615721 

. 

36 

49 

9 

3467 

56786 

8543569 

4678563 

578564877 

10 

7658 

79579 

6975675 

7758868 

853246938 

37 

4 

11 

6784 

95738 

5735487 

8695448 

698765884 

38 

12 

8476 

87359 

7354876 

6948597 

798656448 

13 

7954 

64873 

8877669 

7387638 

674865786 

'2  39 

14 

4597 

48736 

9668877 

8736837 

536978321 

50 

15 

9876 

77854 

6989876 

5548876 

856439554 

40 

16 

6789 

57487 

6798984 

9850438 

987781763 

17 

9987 

97569 

7893968 

6454324 

859658489 

41 

51 

18 

5684 

54365 

3759683 

7587695 

369869756 

19 

6437 

67547 

9764678 

9437685 

456786784 

20 

5984 

73985 

7946342 

4895647 

567865937 

21 

4679 

74628 

3976839 

8376486 

647356893 

22 

8578 

59775 

6583582 

7898769 

638473628 

4.Q 

23 

5684 

46587 

8466839 

5783349 

745947843 

rrO 

24 

7563 

63754 

8593274 

9328795 

598639578 

25 

7689 

86587 

6738531 

3896573 

434696854 

3  44 

26 

8453 

54593 

5864928 

1296859 

876774256 

4.  AC 

27 

7547 

65736 

3656184 

8635853 

337788874 

TCCJ 

28 

6483 

23485 

8377838 

6887369 

586976483 

46  * 

29 

9575 

85627 

5834298 

7637574 

374672175 

:tv 

30 

6439 

59873 

8676936 

9784658 

863938914 

j 

31 

7865 

67896 

5376385 

7383945 

374856387 

In  using  this  table  from  1  to  31  inclusive,  find  the  sum  of  the  hori- 
zontal numbers.  From  32  to  51  inclusive,  find  the  sum  of  the  ver- 
tical numbers  within  the  respective  braces.  From  52  to  56  inclusive, 
find  the  sum  of  the  page  columns. 


CHAPTER  THREE.  177 

LESSSON  XXX. 

SUBTRACTION, 

1.  The  terms  used  in  Subtraction  are  Minuend, 
Subtrahend  and  Difference. 

2.  The  Minuend    is  the  greater  of  the  two  numbers 
given ;  the  Subtrahend  is  the  smaller. 

3.  The  minuend  less  subtrahend  is  the  Difference*  The 
difference  may  be  found  by  either  of  two  ways,  by  diminishing 
the  minuend  by  the  subtrahend,  or  by  increasing  the  subtra- 
hend to  the  minuend.     To  illustrate :     What  is  the  difference 
between  19  and  25?    We  may  say  25  less  19  equals  6,  the 
difference;  or,  we  may  say  19  and  6  are  25,  when  6  is  just  as 
truly  the  difference.     In  either  case,  it  will  be  seen  that  addi- 
tion is  the  one  process  that  is  fundamental. 

4.  The  minuend  is  the  whole  of  which  the  subtrahend  and 
difference  are  the  parts. 

6.  When  the  question  is  of  such  a  nature  as  to  require  the 
part  given  (subtrahend)  to  be  taken  out  of  the  whole  (min- 
uend) what  is  left  is  sometimes  called  the  Remainder. 

6.  Proof:     Observe  that  the   subtrahend   plus   difference 
must  equal  the  minuend. 

7.  How  many  years  must  be  added  to  1885  to  complete  the 
present  century?    What  is  the  minuend?  subtrahend?  differ- 
ence? 

8.  What  is  the  difference  between  seven  7's  and  nine  97s? 
What  is  the  minuend?  subtrahend?  difference? 

9.  A  man  who  owed  f  5000  on  his  house  and  lot  has  made 
8  payments  of  $1000  each.     How  much  does  he  still  owe? 
Give  the  minuend,  subtrahend  and  difference. 

10.  What  number  is  149  less  than  1000?    Is  149  the  sub- 
trahend or  difference? 


178  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XXXI. 


Subtrahend, 
Difference, 

Minuend, 

1. 

125 

2. 

350 

3. 
475 

4. 
641 

1000 

1000 

1000 

1000 

Sub., 

Dif., 
Min., 

5. 

6. 

7. 

8. 

950 
2000 

1050 
2000 

1268 
2000 

1492 
2000 

Min., 
Sub., 
Dif., 

9. 
$185.41 
46.19 

10. 
$150.75 
125.76 

11. 
$1000.00 
100.25 

12. 
$2000.00 
1000.10 

Min., 
Sub., 

Dif., 

13. 
$1241.05 

14. 
9675  Ibs. 

U. 
$150.00 

16. 
113450  mi. 

$   800.50 

2857  Ibs. 

$  19.25 

34844  mi. 

From 
Subtract 

From 

Subtract 

From 
Subtract 

17. 
45009 
18091 

18. 
174620 
90818 

19. 

723608 
518019 

20. 
800000 
376455 

21. 
700060 
508116 

22. 
600460 

278487 

23. 
346571 

184683 

24. 
919645 
820756 

25. 
$19.065 
9.146 

26. 
$20.000 
10.075 

27. 
$200.00 
100.87 

28. 
$5000.00 
3050.25 

CHAPTER  THREE.  179 

LESSON    XXXII. 

1.  What  number  must  be  added  to  6783  to  make  9000? 

2.  What  number  must  be  taken  out  of  12000  to  leave  a 
remainder  of  5629? 

3.  What  number  is  1348  less  than  2500? 

4.  What  number  is  greater  by  568  than  496? 

5.  The  sum  of  two  numbers  is  100000,  one  of   them  is 
50005.      What  is  the  other? 

6.  A  man  owed  $427.50.     He  paid  at  one  time  $125.75, 
at  another  $100,  and  at  another  $50.25.     What  remained 
unpaid? 

7.  A  grain  dealer  bought  5075  bu.  of  wheat  at  one  time, 
and  12300  bu.  at  another.     He  sold  3763  bu.  to  one  custo- 
mer, and  4000  bu.  to  another.     How  many  bushels  had  he 
left? 

8.  A  man  having  $12470  paid  $4070  for  a  house,  $927  for 
furniture,  and  $1000  for  improvements.      How  much  money 
had  he  left? 

9.  Gave   $150  for  a  horse,   $175.84  for  a  carriage,   and 
$62.50  for  a  harness,  and  sold  the  whole  for  $390.50.     What 
was  the  gain? 

10.  A  man  bought  four  city  lots  for  which  he  paid  $15760. 
For  the  first  he  paid  $2175,  for  the  second  $3794,  and  for  the 
third  $4587.     How  much  did  he  pay  for  the  fourth? 

11.  A  speculator  gained  $5760,  and  afterward  lost  $2746; 
at  another  time  he  gained  $3575,  and  then  lost  $4832.    How 
much  did  his  gains  exceed  his  losses? 

12.  Three  men  bought  a  hotel  valued  at  $35680.     The  first 
agreed  to  pay  $7375,  the  second  twice  as  much,  and  the  third 
the  remainder.     What  was  the  third  to  pay? 

13.  A  had  450  sheep,  B  had  175  more  than  A,  and  C  had 
as  many  as  A  and  B  together  minus  114.     How  many  sheep 
hadC? 


180  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XXXIII. 

1.  How  much  greater  is  three  hundred  thousand  five  than 
sixteen  thousand  ninety? 

2.  What  is  the  difference  in  minutes  between  21  days  12 
hours  long,  and  25  days  10  hours  long? 

3.  Subtract  9119  from  118018. 

4.  The  subtrahend  is  260346,  and  the  remainder  72304. 
What  is  the  minuend? 

5.  The  difference  is  $310.62,  and  the  minuend  $1206.28. 
What  is  the  subtrahend? 

6.  What  is  the  sum  of  4062  and  12356  increased  by  the 
difference  between  15000  and  975? 

7.  From  the  sum  of  23462  and  9030,  subtract  the  difference 
between  34000  and  7640. 

8.  From  the  difference  between  19876  and  6032,  subtract 
the  difference  between  12000  and  673. 

9.  From  what  sum  must  $.62  be  taken  to  leave  a  remain- 
der of  $14.60? 

10.  From  8741  subtract  3917. 

11.  How  many  more  than  97865  is  185964? 

12.  1012130  less  808856  equals  what? 

13.  How  many  are  15000  hours  less  8750  hours? 

14.  From  $1.25  take  6  cents  and  nine  mills. 

15.  How  much  does  56173  exceed  17485? 

16.  In  selling  a  quantity  of  flour  for  $7265,  there  was  real- 
ized a  profit  of  $1575.     What  was  the  purchase  price  of  the 
flour? 

17.  In  selling  coal  for    $1950,  $175   was   made.     What 
would  have  been  made  had  the  coal  sold  for  $2176? 

18.  A  man  bought  two  farms,  one  of  136  acres  at  $28  an 
acre,  and  another  of  140  acres  at  $33  an  acre;  he  paid  at  one 
time   $4000,  and  at   another   time   $1875.     How  much  re- 
mained unpaid? 


CHAPTER  THREE.  181 

LESSON    XXXIV. 

1.  The  population  of  Chicago  in  1880  was  491516,  in  1884 
628985.     What  was  the  increase  in  4  years? 

2.  The  population  of  Chicago  in  1870  was  306605,  in  1880 
491516.     At  the  same  rate  of  increase  what  will  be  the  popu- 
lation of  Chicago  in  1890?     In  2000? 

3.  By  the  school  census  of  1884,  the  total  population  of  the 
South  Division  of  Chicago  was  149564;  of  the  North  Divi- 
sion 128490,  and  of  the  West  Division,  351931.     By  how 
much  does  the  population  of  the  West  Division  exceed  the 
united  population  of  the  North  and  South  Divisions? 

4.  The  coal  product  of  the  United  States  in  1884  is  esti- 
mated to  have  been  worth  $131666147.     The  anthracite  of 
Pennsylvania  alone  was  worth  $61436586.     What  was  the 
value  of  the  coal  product  of  the  other  States  combined? 

5.  The  production  of  gold  and  silver  in  the  United  States 
in  1884  amounted  to  a  total  value  of  $79600000.     The  value 
of  the  silver  was  $48800000.     By  how  much  did  the  silver 
exceed  the  gold? 

6.  The  highest  land  elevation  of  Asia  is  29000  ft.,  of  Europe 
is  18500  ft.     What  is  the  difference? 

7.  Chimborazo,  S.  A.,  is  20517  ft.  high;  Mount  St.  Elias, 
N.  A.,  is  17900  ft.  high.      How  much  higher  is  Chimborazo 
than  St.  Elias? 

8.  The  area  of  the  Caspian  Sea  is  132000  sq.  mi. ;  of  Lake 
Superior,  31400  sq.  mi. ;  of  Lake  Michigan,  25600  sq.  mi. ;  of 
Lake  Huron,  23800  sq.  mi. ;  of  Lake  Erie,  10000  sq.  mi. ;  of 
Lake  Ontario,  7300  sq.  mi.     How  much  larger  is  the  Caspian 
Sea  than  the  Great  Lakes  combined? 

9.  The  highest  point  of  land  in  S.  A.  is  23421  ft. ;  in  N.  A. 
17900  ft.     What  is  the  difference  between  the  two  highest 
points  of  Asia  and  Europe  united  and  of  North  and  South 
America  united? 


182  FIRST  BOOK  IX  ARITHMETIC. 

LESSON  XXXV. 

How  many  years  have  elapsed  since  the  date  of  the  follow- 
ing events : 

1.  Battle  of  Bunker  Hill,  1775. 

2.  The  first  bank  established  in  Italy  in  808. 

3.  Anthracite  coal  first  used  for  fuel  in  1768. 

4.  Great  earthquake  at  Lisbon,  1755. 

5.  Joseph  sold  as  a  slave  into  Egypt,  B.  C.  1728. 

6.  Fugitive  slave  law  in  the  United  States,  1850, 

7.  Gas-lights  first  used  in  London,  1807. 

8.  King  Philip's  War,  1675. 

9.  Magna  Charta,  1215. 

10.  First  newspaper  in  America,  1704. 

1.  Express  in  rods  1  mile  less  f  of  a  mile. 

2.  Express  in  quarts  1  bushel  less  f  of  a  bushel. 

3.  What  sum  of  money  is  less  than  $600  by  fy  of  it? 

4.  What  is  the  difference  between  f  of  160  acres  and    f 
of  210  acres? 

5.  From  f  of  $5400  take  £  of  $3600. 

6.  Flour  that  cost  $5600  was  sold  for  f  of  the  cost.     What 
was  the  selling  price? 

7.  A's  age  is  y7-0  of  the  age  of  B,  whose  age  is  3  score  years 
and  10.     What  is  A's  age? 

8.  i7T  of  $13200  is  $300  more  than  was  paid  for  a  farm. 
What  was  the  price  paid  for  the  farm? 

9.  Express  -in  rods  the  difference  between  f  of  a  mile  and 
|  of  a  mile? 

10.  Express  in  square  inches  the  difference  between  \\ 
and  |  of  a  square  foot. 


CHAPTER  THREE.  183 

LESSON    XXXVI. 

The  following  table  will  furnish  a  very  extended  practice 
by  finding  the  difference  between  any  two  numbers.  For  in- 
stance: Find  difference  between  Ex.  4,  Col.  A  and  Ex.  6, 
Col.  B,  etc. 


Col.  A.   Col.  B.    Col.  C.     Col.  D.     Col  E. 

1 

8467 

59873 

854356 

64596837 

678655438 

2 

6784 

79579 

875968 

73878568 

859658489 

3 

8132 

74985 

859327 

94376482 

683964837 

4 

5788 

36587 

176486 

12987369 

374672175 

5 

9005 

57004 

730863 

48958748 

435895689 

6 

3947 

86735 

597089 

69734652 

674578464 

7 

5604 

73007 

837783 

50806530 

860087083 

8 

7039 

80834 

900402 

74057876 

981268538 

9 

6409 

73040 

860547 

59704697 

745947853 

10 

9046 

53836 

732000 

80370702 

607058437 

11 

7304 

74648 

859307 

12875734 

804826573 

12 

8973 

50704 

740634 

61043215 

247659784 

13 

7605 

86880 

327043 

37610123 

736021432 

14 

5078 

90443 

800422 

15489348 

390567493 

15 

9094 

46794 

657387 

53894563 

578556376 

16 

5468 

54038 

598453 

75230706 

867732648 

17 

8005 

62708 

647826 

94673210 

743794485 

18 

3796 

54396 

539473 

58943983 

487645327 

19 

7689 

85631 

946936 

23459876 

568778465 

20 

4794 

78920 

673984 

98762543 

876738564 

21 

5793 

65734 

573036 

56864234 

629315873 

22 

4385 

54598 

659983 

73568365 

548782468 

23 

6932 

67354 

764365 

90030040 

876621743 

24 

9361 

13456 

849530 

53607321 

439864328 

25 

6788 

32147 

603200 

85636543 

580304283 

26 

1238 

41326 

900304 

24317674 

394165708 

27 

5463 

85673 

532060 

50304703 

436487487 

28 

7175 

547H4 

758174 

29658562 

676493678 

29 

5437 

65782 

591826 

65590037 

500300600 

30 

8672 

30564 

307147 

90000550 

734566766 

184  FIRST  BOOK  IN  ARITHMETIC. 

LESSON   XXXVII. 

MULTIPLICATION. 

1.  The  Terms  used  in  Multiplication  are  Multi- 
plicand, Multiplier9  and  Product. 

2.  The  multiplicand  and  multiplier  are  the  Factors  of 
the  product.     When  multiplied  together  they  produce   the 
product. 

3.  The  operation  of  multiplication  consists  in  multiplying 
the  multiplicand   by  the  multiplier,  or,  in  multiplying  the 
factors  together. 

4.  The  sign  of  multiplication  is  X.     When  used  it  should 
be  written  after  the  the  multiplicand,  and  read  multiplied  by. 
$18  x  3.6  is  read  $18  multiplied  by  36,  or  36  times  $18. 

5.  PROOF. — The  best  proof  is  accuracy,  always  accuracy. 
When  pupils  have  learned  division,  they  may  be  required  to 
divide  their  product  by  the  multiplier. 

1.  What  will  75  acres  of  land  cost  at  $125  an  acre? 

2.  What  will  325  horses  cost  at  $175  each? 
8.  At  $37.50  each,  what  will  320  cows  cost? 

4.  Multiply  $420.25  by  305. 

5.  Multiply  $27.70  by  76. 

6.  What  cost  100  tons  of  coal  at  $6.75  a  ton? 

7.  A  barrel  of  flour  weighs  196  Ibs.    How  much  do  48  bbls. 
of  flour  weigh?     What  is  the  multiplicand?     The  multiplier? 
In  the  operation,  is  the  multiplier  48  bbls.  or  48?     What  is 
the  product?     How  would  the  example  be  wrought  by  addi- 
tion?    Which  operation  is  the  shorter,  by  multiplication  or 
addition?     Is   the   product  pounds  or  barrels?     What  is  the 
product  always  like? 

8.  Cost  of  130  sheep  at  $4.80  a  head? 

9.  Cost  of  150  bbls.  of  flour  at  $6.25  per  bbl.? 

10.  Cost  of  338  bbls.  of  pork  at  $11.25  a  bbl.? 


CHAPTER  THREE.  185 

LESSON    XXXVIII. 

1.  What  will  56  acres  of  land  cost  at  $164.50  an  acre? 

2.  What  number  must  be  added  to  272  X  400  to  make  the 
amount  126720? 

3.  At  28  cents  a  pound,  what  will  be  the  cost  of  24  sacks  of 
coffee,  each  containing  64  pounds? 

4.  What  is  the  value  of  107  pieces  of  cloth,  each  piece  con- 
taining 42  yards,  at  $4.28  a  yard? 

5.  How  many  yards  of  shirting  in  49  bales,  each  bale  con- 
taining 26  pieces,  and  each  piece  57  yards? 

6.  What  is  the  cost  of  128  barrels  of  beef,  each  containing 
216  pounds,  worth  13  cents  a  pound? 

7.  Paid  $2709  for  388  barrels  of  flour,  and  sold  the  same 
at  $9.12  a  barrel.     How  much  was  the  gain? 

8.  What  is  the  difference   in   the  cost  of   48  horses  at 
$142.50  each,  and  of  130  sheep  at  $4.80  a  head? 

9.  If  a  man  has  an  income  of  $5670  a  year  and  his  daily 
expenses  average  $7.25,  how  much  can  he  save  in  a  year  of 
365  days? 

10.  If  a  clerk  receives  $1500  salary,  and  pays  $370  for 
board,  $281.50  for  clothing,  $112.90  for  books,  and  $196.65 
for  other  expenses  annually,  what  can  he  save  in  3  years? 

11.  A  merchant  bought  7  hogsheads  of  sugar  at  $46.45  a 
hogshead,  and  sold  it  for  $53.62  a  hogshead.     How  much  did 
he  gain? 

12.  A  man  owing  $15760,  gave  in  payment  5  lots  of  land 
worth  $730  each,  5  horses  valued  at  $236.50  each,  an  inter- 
est he  had  in  a  coal  mine  worth  $2000,  and  $1728.75  in 
money.     How  much  remained  unpaid? 

13.  A  farm  house  is  worth   $3246,  the  farm  is  worth  3 
times  as  much  plus  $1200,  and  the  stock  is  worth  twice  as 
much  as  the  house,  less  $1875.     What  is  the  value  of  the 
whole,  and  of  the  farm  and  stock? 


186  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XXXIX. 

1.  Find  the  cost  of  386  railway  coaches  at  $7034.75  each. 

2.  What  cost  802  tubs  of  butter  at  $27.08  each? 

3.  What  will  be  the  cost  of  building  a  line  of  telegraph  274 
miles  long  at  $967  a  mile? 

4.  If  1049  pounds  of  seed  cotton  be  raised  from  an  acre  of 
land,  how  many  pounds  will  386  acres  produce? 

5.  If  a  cotton  mill  manufactures  628  yards  of  cloth  in  a  day, 
how  many  yards  can  it  make  in  297  days? 

6.  If  a  garrison  of  soldiers  consume  5789  pounds  of  bread 
a  day,  how  much  will  they  consume  in  237  days? 

7.  How  many  oranges  in  356  boxes,  each  box  containing 
264  oranges? 

8.  Three  schooners  ship  239  cords  of  wood  each,  and  a 
fourth  ships  248  cords.     What  is  the  value  of  the  whole  at 
$4.25  a  cord? 

9.  If  it  requires  108  tons  of  iron  rail  for  1  mile  of  track,  how 
many  tons  will  be  required  for  476  miles,  and  what  will  be  its 
value  at  $145  a  ton? 

10.     A  crop  of  cotton  was  put  up  in  472  bales,  the  average 
weight  of  which  was  588  pounds.      What  was  the  weight  of 

the  whole  crop  and  its  value  at  18  cents  a  pound? 
What  is  the  product : 

11.  Of  2572  bushels  by  94?  21.  Of  408091  by  2407? 

12.  Of  $403.06  by  127?  22.  Of  73069  by  46035? 

13.  Of  86072  pounds  by  208?  23.  Of  $4.72  by  100? 

14.  Of  316  times  $487.46?  24.  Of  $30.40  by  60? 

15.  Of  507  times  30975  days?  25.  Of  $1200  by  700? 

16.  Of  325  times  6408  cents?  26.  Of  42030090 x  3020? 

17.  Of  370607  by  4971?  27.  Of  120  times  5000? 

18.  Of  600326  by  2645?  28.  Of  600  times  21000? 

19.  Of  730096  by  5006?  29.  Of  1000  times  104000? 

20.  Of  2407068  by  3406?  30.  Of  7000600  x  50040? 


CHAPTER  THREE.  187 

LESSON    XL. 

1.  The  factors  are  4576  and  239.     What  is  the  product? 

2.  What  is  the  product  of  the  factors  31,  41  and  51? 

3.  How  many  acres  are  there  in  225  farms  of  225  acres 
each? 

4.  What  will  75  tubs  of  maple  sugar  cost,  each  tub  con- 
taining 75  Ibs.,  at  $0.15  a  pound? 

<5.  A  capitalist  bought  5  farms  :  One  of  206  acres,  at  $69 
per  acre;  one  of  239  acres  at  $58  per  acre;  one  of  337  acres 
at  $75  per  acre;  one  of  368  acres  at  $87  per  acre,  and  one  of 
416  acres  at  $98  per  acre.  After  paying  $125000  how  much 
did  he  owe  ? 

6.  How  many  feet  are  there  in  569  miles? 

7.  If  two  ships  start  from  the  same  port  and  sail  in  oppo- 
site directions,  one  69  miles  a  day  and  the  other  78  miles  a 
day,  how  far  apart  will  they  be  after  sailing  29  days? 

8.  Two  ships  sail  from  distant  ports- and  sail  toward  each 
other  at  the  rate  of  68  and  73  miles  a  day  respectively.    They 
meet  at  the  close  of  the  19th  day.     How  far  apart  were  they 
at  starting? 

9.  A  farm  of  176  acres  was  bought  for  $59  an  acre;  it  was 
sold  at  an  advance  of  $18  an  acre.     What  was  the  gain  and 
what  did  the  farm  sell  for? 

10.  A.  merchant  bought  a  quantity  of  flour  for  $6789.     He 
sold  it  at  an  advance  of  J  of  the  cost  less  $467.     What  was 
the  gain  and  what  was  the  selling  price? 

11.  A  merchant  bought  500  bbls.  of  flour  at  $4.75  a  bbl. 
He  sold  116  bbls.  for  $4.87£  a  bbl.,  125  bbls.   for  $5.25  a 
bbl.,  and  the  remainder  for  $5.63  a  bbl.     What  was  the  entire 
gain? 

12.  What  will  be  the  cost  of  5  bales  of  cloth,  each  bale 
containing  15  pieces,  and  each  piece  measuring  26  yards,  at 
$1.75  a  yard? 


188  FIRST  BOOK  IN  ARITHMETIC. 


LESSON    XLI. 


ALIQUOT  PARTS  OF  ONE  DOLLAR. 


5  cents  —  ^  of  $1. 
10  cents  =  T10  of  $1. 
20  cents  =  -J  of  $1. 
25  cents  =  \  of  $1. 
50  cents  =  1  of  SI. 


2 


6|-  cents  =  ^  of  $1. 

81  cents  =  ^  of  $1. 

12-|  cents  =  _j.  of  §lt 

16|  cents  =  J   of  $1. 
"831  cents  ==  -i   of  $1. 


1.  At  6^  cents  a  Ib.  for  sugar,  how  many  Ibs.  can  be  bought 
for  fl? 

2.  What  will  48  oranges  cost  at  6£  cents  each? 

3.  At  8J  cents  each,  how  many  copy  books  can  be  bought 
for  $1? 

4.  Cost  of  5  dozen  copy  books  at  8^  cents  each? 

5.  At  12J  cents  a  Ib.  for  maple  sugar,  how  many  Ibs.  will 
$1  buy? 

6.  Cost  of  a  tub  of  maple  sugar,  weighing  72  Ibs.  net,  at 
12£  cents  a  Ib.  ? 

7.  At  16f  cents  a  dozen  for  eggs,  how  many  eggs  can  you 
buy  for  $1? 

8.  What  will  96  yards  of  ribbon  cost  at  16f  cents  a  yard? 

9.  At  33J  cents  a  Ib.  for  coffee,  how  many  Ibs.  can  you  buy 
for  $1?  $2?  |3?  $7?  $25? 

10.  At  33J  cents  a  bu.  for  oats,  what  will  33   bu.  cost? 
42  bu.?  420  bu.? 

11.  At  6^  cents  each  for  drawing  pencils,  how  many  can 
be  bought  for  $48? 

ANALYSIS.    At  6i  cents  a  piece  $1  will  buy  16  pencils.     Then  $48 
will  buy  48  times  16  pencils. 

12.  At  12^  cents  a  yard  how  many  yards  of  calico  will  27 
Ibs.  of  butter  at  33^  cents  a  Ib.  pay  for? 

13.  Cost  of  160  Ibs.  of  sugar  at  6£  cents  a  Ib.?  at  8J  cents? 
at  12    cents? 


CHAPTER  THREE.  189 

LESSON    XLII. 

1.  A   Debt  is   that  which  is  due   from   one   person  to 
another,  whether  money,  goods,  or  service. 

2.  A  Debtor  is  a  person  who  owes  another  either  money, 
goods,  or  service. 

3.  A  Creditor  is  one  to  whom  the  money,  merchandise, 
or  service  is  due. 

4.  A  Bill  is  an  account  of  goods  sold  or  service  rendered 
with  the  price  annexed  to  each  item. 

6.  The  letter  @  in  bills  means  "  at,"  and  is  followed  by  the 
price  of  one  of  the  things  named  in  the  item. 

6.  To  extend  a  bill  is  to  find  the  price  of  the  several  quanti- 
ties itemized. 

7.  To  foot  a  bill  is  to  add  the  extended  column. 

8.  To  receipt  a  bill  is  to  write  "Paid"  or  " Keceived  Pay- 
ment" at  the  bottom  of  the  bill  together  with  the  name  of  the 
Creditor. 

NOTE. — Bills  are  usually  receipted  by  the   Cashier.     Any  Clerk 
authorized  to  receive  money  may  receipt  a  bill. 

9.  CHICAGO,  May  6,  1885. 
MRS.  AYERS,  No.  2000  Dearborn  Avenue, ' 

Bought  of  M.  A.  SWIFT  &  Co. 


Mav 

5 

&  i 

00 

1  Skirt,           

i 

75 

9  Yds.  Cashmere,  @,  40  cts.      .        .     •    . 
4£  Yds.  Kibbon,  @  20  cts  
4  Vests,  @.  $1.25,         

3 
5 

60 
90 
00 

$  12 

25 

This  bill  was  settled  on  June  1.     The  Cashier  received 
the  money  and  wrote  at  the  bottom  of  the  bill  a  receipt,  as 

follows: 

Paid  June  1.  M.  A.  SWIFT  &  Co. 

By  H.  J. 


190 


FIRST  BOOK  IN  ARITHMETIC, 


LESSON     XLIII. 

CHICAGO,  Aug.  7,  1885. 
MK.  J.  S.  MILLS,  Aurora,  111., 

Bo't  of  LEONARD  BACON  &  Co. 


Aug. 

15 

12  yds.  Broadcloth,  .     .     . 

.     .     @  $2  25 

$27 

00 

18    "    Cassimere,    .     . 

.     .      "      1.75 

31 

^o 

10    "    Satinet,     .    . 

"      1  124 

11 

25 

42     "    Flannel,    .     . 

.     .      "          50 

21 

00 

35     "     Silk,     

.     .      "      1.18 

41 

30 

$132 

05 

Eeceived  Payment,  Sept.  1. 


LEONARD  BACON  &  Co. 

By  A.  H.  S. 


Make  out  bills,  extend,  foot,  and  receipt,  the  first  of  the 
month  following  the  purchase: 


1.  8  Ibs.  Ham, 
12  Ibs.  Veal,     . 

16  Ibs.  Mutton,     .    *    . 

11  Ibs.  Beef,     . 

12  Ibs.  Pork, 

2.  10  Hams,  18  Ibs.,     . 
10  Dried  Beef,  13  Ibs., 
25  Ibs.  Codfish, 

16  Ibs.  Mackerel, 
16  Ibs.Bacon, 

3.  36  yds.  Calico,      . 
64  Spools  Thread,     . 
75  yds.  Sheeting, 

48  yds.  Cassimere,    . 
4  Table-cloths, 


.16 
.16 
.18 
.22 

•84 

.17 
.18 
.11 


•6* 

.18 

$2.25 
1.85 


CHAPTER  THREE. 


191 


4.  112  bbls.  Flour, 
108  tons  Hay, 
225  bu.  Wheat, 
417  bu.  Corn, 
130  bu.  Barley, 

75  bu.  Eye, 

5.  12  doz.  Eggs, 
12  doz.  Eggs, 
48  Ibs.  Coffee, 
15  Ibs.  Butter, 
82  Ibs.  Cheese, 

6. 


@$5.75 
"   13. 

"       .92 


"       .83 

"       .94 

"       .121 


"       .25 


Sept. 

3 

To  5  Blank  Books,      . 

@  $2.30 

u 

** 

"   7  gross  Spencerian  Pens, 

"     1.12 

a 

26 

"   15  B.  &  S.  Bookkeeping,      . 

*      1.75 

Oct. 

10 

M  4  reams  Cap  Paper, 

"      3.40 

u 

19 

"   20  Townsend's  Com.  Law,  . 

"      2.87 

Nov. 

22 

"    12  packs  Plain  Cards, 

.37 

Dec. 

4 

"  Note  Paper  and  Ink, 

u 

2 

78 

$ 

Received  Payment  by  note  at  30  days,  Jan.  2,  1885. 


7. 


15  yds  Broadcloth,   . 

@,  $4.20 

24    "     Satinet,      ...» 

"      1.37£ 

10    '     Vesting, 

.90 

42    "    Flannel,      .... 

"       .75 

60     "    Drilling, 

.16 

12    tt     Silk,            .... 

"      2.62^ 

38    "     Ticking, 

a        .52 

— 

192 

8. 

FIRST  BOOK  IN  ARITHMETIC. 

Jan. 

6 

For  Building  Barn,  as  per  contract,    . 

$450 

« 

« 

40 

75 

Mch. 

20 

"     15  days'  work  of  self,     .        .     @  $3| 

" 

" 

"     7      "          "of  son,         .          "      1.50 

April 

16 

«     2      "          "...."      3.50 

u 

« 

"    Nails,  Hinges  and  Sundries, 

150 

$ 

LESSON    XLIV. 

1.  Make  a  bill  of  the  books  and  stationery  used  in  the 
Fourth  Grade. 

2.  Make  a  bill  of  7  items  bought  of  your  grocer,  amounting 
to  not  less  than  $5.     Let  the  items  be  appropriate  in  quantity 
and  price. 

3.  Make  a  bill  of  7  items  bought  at  a  retail  dry  goods  store. 
Let  the  goods   be   bought  on  three  consecutive    Saturdays. 
Amount  of  bill  not  less  than  $10. 

4.  Make  a  bill  of  5  items  bought  at  a  flour  and  feed  store. 
Buy  at  wholesale.     Bill  to  amount  to  $  1000.     Consult  com- 
mercial column  of  daily  paper  for  current  prices. 

6.  Make  a  bill  of  5  items  bought  at  a  retail  hardware  store — 
$25. 

6.  Make  a  bill  of  7  items  bought  on  South  Water  street. 
Consult  daily  paper  for  prices. 

7.  Make   a  bill  of   $7000  bought  at  a  wholesale  grocery 
house.     Let  the  quantity  of  the  items  be  well   considered. 
Consult  daily  paper  for  prices — 10  items. 

8.  Make  a  bill  for  a  set  of  crockery  sufficient  for  housekeep- 
ing.    The  amount  of  bill  may  vary  from  $25  to  $150. 

9.  Make  a  bill  for  10  different  books  you  would  like  to  own. 
Let  the  prices  be  current.     Let  the  purchases  be  made  on  four 
consecutive  Saturdays. 


CHAPTER  THREE.  193 

LESSON    XLV. 

MISCELLANEOUS. 

1.  How  much  heavier  is  |  of  a  pound  of  gold  than  |  of  a 
pound? 

2.  How  much  less  is   |  of  a  day  than  |  of  a  day? 

3.  How  much  less  is  |  of  a  pound  of  coffee  than  J  of  a 
pound? 

4.  How  much  greater  is  -|  of  a  hogshead  of  wine  than  | 
of  it? 

6.  How  many  times  -1  of  a  hogshead  of  molasses  is  -|  of  it? 

6.  How  much  less  is  -|  of  a  square  yard  of  carpet  than  | 
of  it? 

7.  Out  of  £  of  a  peck  of  oats  1  of  a  peck  was  taken.     How 
many  quarts  were  left? 

8.  How  many  times  £  of  a  peck  of  corn  are  6  bushels? 

9.  How  many  times  are  |  of  a  peck  in  5  pecks? 

10.  What  is  the  weight  of  5  gold  rings,  each  weighing  | 
of  an  ounce? 

11.  &  of  an  ounce  of  gold  is  how  much  greater  than  ^  of  it? 

12.  -|  of  a  pound  of  tea  is  how  much  greater  than  |  of  it? 

13.  JL  Of  an  hour  is  how  much  less  than  -|  of  it? 

14.  49  months  are  how  many  times  ^  of  a  year? 

15.  ±  of  a  ton  of  hay  is  how  many  times  -^  of  a  ton? 

16.  How  much  time  elapses  from  9  o'clock  A.  M.  to  12  M.? 

17.  How  much  time  elapses  from  10  o'clock  A.  M.  to  8  p.  M.? 

18.  How  much  time  is  from  9-30  o'clock  A.  M.  to  2-30  P.  M.? 

19.  How  much  time  is  from  9-40  o'clock  A.  M.  to  2  20  P.  M.  ? 

20.  How  much  greater  is  the  time  from  10-15  A.  M.  to  2  45 
p.  M.,  than  from  10-45  A.  M.  to  2-15  p.  M.? 

21.  What  is  the  time  from  2-30  p.  M.  Monday,  to  9-15  A.  M. 
Tuesday? 


194  FIRST  BOOK  IN  ARITHMETIC. 

LESSON   XLVI. 
SQUARE  MEASURE. 


1  square  mile=640  acres. 
1  acre=160  square  rods. 
1  square  rod=30^-  sq.  yards. 
1  square  yard=9  square  feet. 
1  square  foot=144  sq.  inches. 


144  square  inches =1  sq.  foot. 

9  square  feet=l  sq.  yard. 
30][  sq.  yards=l  sq.  rod. 
160  square  rods=l  acre. 
640  acres=l  square  mile. 


1.  3  square  yards  equal  how  many  square  feet? 

2.  54  square  feet  equal  how  many  square  yards  ?  72  square 
feet? 

3.  y%  of  a  square  foot  equals  how  many  square  inches  ? 

4.  \  acre  equals  how  many  square  rods  ?    |  acre  ? 
<5.   £  of  an  acre  equals  how  many  square  rods? 

6.  |  of  an  acre  equals  how  many  square  rods? 

7.  12  square  inches  equal  what  part  of  a  square  foot? 

8.  3  square  feet  equal  what  part  of  2  square  yards  ? 

9.  3  square  feet  equal  -§-  of  how  many  square  yards? 

10.  |  of  a  square  mile  equals  how  many  acres? 

11.  jo  of  a  square  mile  equals  how  many  acres? 

12.  6  square  feet  equals  what  part  of  4  square  yards? 

13.  1  square  yard  equals  what  part  of  45  square  feet? 

14.  40  square  rods  equal  \-  of  how  many  acres? 

15.  9  square  yards  10  square  feet  eqaal  how  many  square 
reet? 

16.  12  square  feet  equal  \  of  how  many  square  yards? 

1 7.  How  much  greater  is  5  square  yards  than  36  square  feet? 

18.  How  much  less  is  y^  of  a  square  foot  than  20  square 
inches? 

19.  115  square  feet  equal  how  many  square  yards? 


CHAPTER  THREE.  195 

LESSON    XLVII. 

CUBIC    MEASURE. 


1  Cord=128  Cubic  Feet. 

1  Cubic  Yard= 27  Cubic  Feet. 

1  Cubic  Ft.  =  l  728  Cu.  Inches. 


1728  Cubic  Inches=l  Cu.  Ft. 
27  Cu.  Ft.  =  1  Cubic  Yard. 
128  Cu.  Ft.  =  l  Cord. 


1.  2  cubic  yards  6  cubic  feet  equal  how  many  cubic  feet? 

2.  3  of  a  cubic  yard  equals  how  many  cubic  feet?     |  ? 

3.  -J-  of  a  cubic  yard  equals  how  many  cubic  feet?     f  ? 

4.  |-  of  a  cubic  yard  is  how  much  greater  than  |  of  a  cubic 
yard? 

5.  6  cubic  feet  is  what  part  of  2  cubic  yards?     9  cubic  feet? 

6.  9  cubic  feet  is  |  of  how  many  cubic  yards?    3  cubic  feet? 

7.  \  of  a  cord  equals  how  many  cubic  feet? 

8.  ^  of  a  cord  equals  how  many  cubic  feet? 

9.  A  cord  is  a  pile  of  wood  8  feet  long,  4  feet  wide  and  4 
feet  high.     What  part  of  a  cord  is  in  4  feet  of  the  same  pile? 


AREAS. 
The  amount  of  surface  in  figures  like  the  following 


is  called  the  Area.  Area  is  always  expressed  in  sq.  in.,  sq.  ft., 
sq.  yd.,  sq.  rd.,  etc.,  and  is  equal  to  the  product  of  the  length 
of  the  surface  multiplied  by  the  width,  as  :  the  area  of  a  slate 
12  inches  long  and  8  inches  wide  is  96  square  inches. 

1.  What  is  the  area  of  a  slate  9  inches  long  and  6  in.  wide? 

2.  What  is  the  area  of  a  table  8  feet  long  and  4  feet  ffide  ? 

3.  What  is  the  area  of  a  floor  6  yards  long  and  5  yards  wide? 

4.  What  is  the  area  of  a  garden  12  rods  long  and  9  rods  wide  ? 

5.  How  many  square  feet  are  in  a  board  12  feet  long  and  12 
inches  wide  ? 


106  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    XLVIII. 

1.  What  is  the  area  of  one  side  of  a  slate  12  inches  long 
and  7  inches  wide  ? 

2.  What  is  the  area  of  one  side  of  a  leaf  of  writing  paper  9 
inches  long  and  8  inches  wide? 

3.  A  blackboard  is  12  feet  long  and  4  feet  wide.     What  is 
its  area? 

4.  How  many  square  yards  equal  the  ceiling  of  a  room  8 
yards  long  and  5  yards  wide  ? 

5.  How  many  square  yards  equal  a  blackboard  9  feet  long 
and  5  feet  wide? 

6.  How  many  square  feet  in  a  surface  12  inches  long  and 
12  inches  wide? 

7.  What  is  the  area  of  a  field  12  rods  long  and  8  rods  wide? 

8.  A  field  10  rods  long  contains  80  square  rods.    How  wide 
is  it? 

9.  A  blackboard  whose  area  is  24  square  feet  is  3  feet  wide. 
How  long  is  it? 

10.  What  part  of  a  square  foot  is  a  surface  4  inches  long 
and  3  inches  wide? 

11.  What  part  of  a  square  yard  is  a  surface  2  feet  long  and 
2  feet  wide? 

12.  At  8  cents  a  square  foot  what  is  the  cost  of  making  a 
blackboard  4  feet  long  and  3  feet  wide? 

13.  At  9  cents  a  square  inch  what  is  the  cost  of  finishing  a 
binding  3  inches  long  and  3  inches  wide? 

14.  At  $1  a  square  yard  what  is  the  cost  of  painting  the 
ceiling  of  a  room  4  yards  long  and  3  yards  wide? 

15.  At  9  cents  a  square  yard  what  is  the  cost  of  painting  a 
floor  9  feet  wide  and  12  feet  long? 

16.  What  part  of  an  acre  does  a  field  contain  that  is  10 
rods  long  and  8  rods  wide? 


CHAPTER  THREE.  197 

LESSON    XLIX. 

REDUCTION  BY   MULTIPLICATION. 

1.  How  many  inches  in  26  rd.,  3  yd.,  2  ft.,  9  in.? 

2.  How  many  feet  in  7  fur.,  30  rd.,  4  yd.? 

3.  How  many  pints  in  6  bu.,  3  pk.,  6  qt.  ? 

4.  How  many  pennyweights  in  4  lb.,  9  oz  ,  12  pwt.? 

5.  How  many  quarts  in  2  hhd.,  24  gal.,  3  qt.? 

6.  How  many  minutes  in  4  wk.,  3  da.,  5  hr.? 

7.  How  many  square  inches  in  14  sq.  yd.,  5  sq.  ft.? 

8.  How  many  cubic  inches  in  5  cu.  yd.  ? 

9.  How  many  pounds  in  4  T.,  12  cvvt.,  60  lb.? 

10.  How  many  ounces  in  6  cwt.,  28  lb.,  10  oz.? 

11.  Reduce  3  mi.,  226  rd.  to  feet. 

12.  Eeduce  4  cwt.,  10  lb.  to  ounces. 

13.  Reduce  10  lb.,  10  oz.  to  pennyweights. 

14.  Reduce  25  gal.,  1  qt   to  pints. 

15.  Reduce  50  bu.,  3  pk.  to  quarts. 

16.  Reduce  25  cords  to  cubic  feet. 

17.  Reduce  the  month  of  August  to  minutes. 

18.  Reduce  14  A.  to  square  rods. 

19.  Reduce  10  sq.  mi.  to  acres. 

20.  Reduce  40  rd.,  5  yd.  to  feet. 

21.  Change  25  rni.  to  feet. 

22.  Change  50  bu.  of  wheat  to  pounds. 

23.  Change  4  perches  of  stone  to  cubic  inches. 

24.  Change  40  T.  to  pounds. 

25.  Change  100  acres  to  square  rods. 

26.  Change  25  hhd.  to  gallons. 

27.  Change  25  bbls.  of  flour  to  pounds. 

28.  Change  80  bu.  of  oats  to  pounds. 


198  FIRST  BOOK  IN  ARITHMETIC. 

LESSON     L. 

1.  A  pile  of  wood  8  ft.  long,  4  ft.  wide  and  4  ft.  high  con- 
tains a  cord.     How  many  cubic  feet  in  a  cord? 

2.  How  many  cords  are  there  in  a  pile  of  wood  24  ft.  long, 
4  ft.  wide  and  4  ft.  high? 

3.  How  many  cords  of  wood  in  5  piles,  each  pile  being  48 
ft.  long,  8  ft.  high  and  4  ft.  wide? 

4.  There  is  a  shed  32  ft.  long,  20  ft.  wide  and  12  ft.  high. 
Find  the  value  of  the  wood  that  can  be  piled  in  the  shed  when 
wood  sells  at  $15  a  cord. 

6.  How  many  square  feet  are  there  in  a  board  that  is  15  ft. 
long  and  12  in.  wide? 

6.  How  many  square  feet  of  floor  would  12  such  boards 
make? 

7.  There  is  a  blackboard  86  ft.  long  and  8  ft.  wide.     How 
many  square  yards  of  surface  does  the  board  measure? 

8.  How  many  square  yards  of  surface  in  12  such  boards? 

9.  How  many  square  yards  of  ceiling  in  a  room  18  ft.  long 
by  15  ft.  wide? 

10.  How  many  yards  of  carpet  a  yard  wide  would  be  re- 
quired for  the  floor  of  a  hall  60  ft.  long  by  42  ft.  wide? 

11.  What  would  the  carpet  cost  at  85  cts.  a  yard? 

12.  How  many  square  yards  of  surface  will  one  side  of  a 
room  21  ft.  long  and  15  ft.  high  measure?     2  sides? 

13.  If  the  room  is  18  ft.  wide  what  would  the  other  two 
wall  surfaces  measure? 

14.  How  many  plastered  surfaces  are  there  in  your  school 
room?     Name  them. 

15.  How  many  square  rods  in  a  field  90  rods  long  and  75 
rods  wide?     How  many  acres? 

16.  How  much  will  it  cost  to  dig  a  cellar  24  feet  long,  18 
feet  wide,  and  6  feet  deep,  at  1  cent  a  cubic  foot? 

17.  How  many  square  feet  in  1  acre? 


CHAPTER  THREE.  199 

LESSON    LI. 

DIVISION. 

1.  The  terms  used  in  division  are  Dividend,  Divi- 
sor,  Quotient  and  Remainder. 

2.  We  divide  the  dividend  by  the  divisor  to  obtain  the  quo- 
tient. 

3.  When  the  dividend  is  something  more  than  the  product 
of  the  divisor  and  quotient,  the  part  in  excess  of  such  product 
is  called  remainder.     The  remainder  is  an  undivided  part  of 
the  dividend. 

4.  PROOF. — Multiply  quotient  by  divisor.     If  there  be  no 
remainder,  the  product  should  equal  the  dividend.     If  there 
be  a  remainder,  it  must  be  added  to  such  product  to  get  the 
dividend. 

5.  The  sign  of  division  is  made  thus:    H-.     It  is  read: 
divided  by  or  divided  into. 

6.  An  operation  of  division  may  be  expressed  in  three  ways. 
Let  it  be  required  to  divide  480  bbls.  of  flour  into  16  equal 
lots.     The  operation  may  be  expressed  thus: 

480  bbls.  -r-  16  =  ?     or  thus:   16)480~bbls.         48Q 
or  by  writing  the  dividend  over  the  divisor,  thus:   — j|r 

The  first  expression  makes  with  the  answer  an  equation, 
and  should  be  used  when  the  quotient  can  be  written  at  sight. 

The  second  expression  is  the  usual  one  when  the  several 
steps  in  the  operation  are  necessarily  written  out. 

The  third  is  the  fractional  form,  and  should  be  used  when 
the  operation  can  be  shortened  by  cancellation. 

7.  4000  -T-      20  =  $  2500  -r-    50  = 
6000  -r-    300  =  $18000  --      9  = 

12000  -i-  4000  =  $  8100  -=-  900  = 

8.  26)3328  27)125~55  28)16128 


200  FIRST  BOOK  IN  ARITHMETIC. 

8x9_       %  12xl2_          26x45_ 
3x8~       *  11x12"          13.x  9  ~ 

10.  How  many  times  is  29  contained  in  68468? 

OPERATION:  SUGGESTION: 

By  inspecting  the  operation, 

29)68468  it  wni  be  seen  that  the  last  par- 

tial dividend  is  28;  one  less  than 
the  divisor.     28  is  the  remain- 


176  ' 

174  PROOF.    2360x29=68440. 

28  68440+28=68468. 


LESSON    LII. 

1.  How  long  can  60  men  subsist  on  an  amount  of  food  that 
will  last  1  man  7620  days? 

2.  How  many  tons  of  hay  at  $26  a  ton  must  be  given  for 
24  cows  worth  $32  a  head? 

3.  How  many  casks,  each  holding  81  gallons,  can  be  filled 
from  14  pipes  of  wine,  each  containing  124  gallons? 

4.  Bought  150  acres  of  land  for  $7650,  and  sold  it  for  $63 
an  acre.     How  much  was  the  whole  gain? 

5.  What  number  divided  by  95  will  give  a  quotient  of  75, 
and  a  remainder  of  47  ? 

6.  How  long  would  it  take  a  train  of  cars,  going  at  an 
average  rate  of  40  miles  an  hour,  to  travel  around  the  earth 
at  the  equator,  the  distance  being  24898  miles? 

7.  If  100  barrels  of  flour  cost  $600,  what  will  350  barrels 
cost  at  the  same  rate? 

8.  How  many  bales,  each  weighing  510  pounds,  can  be 
made  of  76500  pounds  of  cotton? 


CHAPTER  THREE.  201 

LESSON    LIII. 

2.  The  product  of  two  numbers  is  8928,  and  one  of  the 
numbers  is  72;  what  is  the  other  number? 

2.  The  dividend  is  7280,  and  the  quotient  is  208;  what  is 
the  divisor? 

3.  A  man  sold  6  horses  at  $125  each,  25  head  of  cattle  at 
$30  each,  and  with  the  proceeds  bought  land  at  $25  an  acre; 
how  many  acres  did  he  buy? 

4.  How  many  pounds  of  cheese,  worth  10  cents  a  pound, 
can  be  bought  for  22  pounds  of  butter,  worth  15  cents  a  pound? 

5.  If  56  yards  of  cloth  cost  $336,  how  much  will  12  yards 
cost  at  the  same  rate? 

6.  If  I  buy  225  barrels  of  flour  for  $2025,  and  sell  the 
same  for  $1800,  how  much  do  I  lose  on  each  barrel? 

7.  A  man  sold  his  house  and  lot  for  $5670  and  took  his 
pay  in  bank  stock  at  $90  a  share;  how  many  shares  did  he 
receive  ? 

8.  How  many  pounds  of  tea,  worth  75  cents  a  pound,  ought 
a  man  to  receive  in  exchange  for  27  bushels  of  oats,  worth  50 
cents  a  bushel? 

9.  The  quotient  of  one  number  divided  by  another  is  40,  the 
divisor  is  364,  and  the  remainder  120;  what  is  the  dividend? 

10.  How  many  tons  of  hay  at  $12  a  ton,  must  be  given  for 
21  cows  at  $24  apiece? 

11.  A  tobacconist  has  6324  pounds  of  tobacco,  which  he 
wishes  to  pack  in  boxes  containing  62  pounds  each;    how 
many  boxes  must  he  procure  to  contain  it?      » 

12.  How  many  horses  at   $260  each,   can  be  bought  for 
$19500? 

13.  A  drover  received  $26460  for  196  head  of  cattle.     How 
much  was  their  average  value  a  head? 

14.  If  43776  pounds  of  cotton  be  packed  in  96  bales,  what 
is  the  average  weight  of  each  bale? 


202  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    LIV. 

1.  In  94185  yards  of  sheeting  are  how  many  pieces,  each 
containing  45  yards? 

2.  A  planter  raised  43240  pounds  of  cotton  on  94  acres. 
What  was  the  average  number  of  pounds  to  the  acre? 

3.  A  man  bought  114  acres  of  land  for  4104  dollars;  what 
was  the  average  price  per  acre? 

4.  Nine  thousand  dollars  was  paid  to  75  operatives;  what 
did  each  receive? 

5.  There  are  24  hours  in  a  day;  how  many  days  in  11424 
hours? 

6.  In  one  hogshead  are  63  gallons;   how  many  hogsheads 
in  6615  gallons? 

7.  If  a  man  travel  48  miles  a  day,  how  long  will  it  take 
him  to  travel  1296  miles? 

8.  A  garrison  consumed  1712  barrels  of  flour  in  107  days; 
how  much  was  that  per  day? 

9.  How  long  would  it  take  a  vessel  to  sail  from  New  York 
to  China,  allowing  the  distance  to  be  9072  miles,  and  the  ship 
to  sail  144  miles  a  day? 

10.  How  long  could  27  men  subsist  on  a  stock  of  provision 
that  would  last  1  man  3456  days? 

11.  A  drover  received  10362  dollars  for  314  head  of  cattle; 
what  was  their  average  value  per  head? 

12.  If  42864  pounds  of  cotton  be  packed  in  94  bales,  what 
is  the  average  weight  of  each  bale? 

13.  If  a  field  containing  42  acres  produce  1659  bushels  of 
wheat,  what  will  be  the  number  of  bushels  per  acre? 

14.  In  what  time  will  a  reservoir  containing  109440  gal- 
lons, be  emptied  by  a  pump  discharging  608  gallons  per  hour? 

15.  What  number  besides  216  will  divide  75168  without  a 
remainder? 


CHAPTER  THREE. 


203 


LESSON    LV. 

1.  At  8  cents  a  pound,  how  many  pounds  of  sugar  can  be 
bought  for  $16? 

SUGGESTION:    1600  cents  -s-  8  cents  —  1600  -*-  8  =  200. 

2.,  At  25  cents  a  bushel,  how  many  potatoes  will  $250  buy? 

3.  At  32  cents  a  pound  for  coffee,  how  much  can  be  bought 
for  $288? 

4.  At  $2.25  a  barrel  for  apples,  how  many  apples  can  be 
purchased  for  $40.50?     $405?     $4050? 

6.  At  $5.75  a  barrel  for  flour,  how  much  flour  will  $97.75 
buy?     $977.50?     $9775? 

6.  If  64  bushels  of  wheat  cost  $80.00,  what  is  the  cost  of 
one  bushel? 

7.  If  10  barrels  of  apples  cost  $22.75,  what  will  40  barrels 
cost? 

8.  If  100  acres  of  land  cost  $2675,  what  is  the  cost  per 
acre? 

9.  Divide  $5. 60  by  8. 

10.  When  252  pounds  of  butter  sell  for  $84,  what  should 
42  pounds  sell  for? 

Find  quotients  and  remainders.     Prove  the  results. 


1.  4636  - 

-  56. 

11.  7943- 

-  54. 

21.  32465- 

-38. 

2.  6324  - 

-28. 

12.  4826- 

-  49. 

22.  16849  - 

-38. 

3.  2583  - 

-32. 

13.  7244  - 

-  36. 

23.  27548- 

-43. 

4.  4428- 

-37. 

14.  6549  - 

-47. 

24.  39641  - 

-  54. 

5.  8229  - 

-93. 

15.  7319  - 

-87. 

25.  48564- 

-63. 

6.  2348- 

-  53. 

16.  8125  - 

-  92. 

26.  56103- 

-68. 

7.  9748- 

-48. 

17.  7687- 

-83. 

27.  65047- 

-69. 

8.  2714  - 

-39. 

18.  5462- 

-72. 

28.  74326  - 

-75. 

9.  7228  - 

-66. 

19.  6553- 

-79. 

29.  84408  - 

-89. 

10.  8349  - 

-62. 

20.  3814  - 

-43.' 

30.  90865  - 

-95. 

204  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    LVI. 

1.  If  $6250  are  paid  for  25  horses,  how  many  horses  at  the 
same  average  price  can  be  bought  for  $32000? 

2.  If  12  shares  of  city  railway  stock  cost  $2616,  how  many 
shares  will  $104640  buy? 

3.  An  agent  had   $6000  with  which   to  buy  flour.     His 
expenses  were  $112.     He  was  allowed  $75  for  his  services. 
He  bought  1000  barrels  of  flour  and  had  $313  left.     What 
price  per  barrel  was  paid  for  the  flour? 

4.  A  man  owns  328  acres  of  land,  worth  $38704,  and  298 
shares  of  bank  stock  worth  $40528.     What  is  the  difference 
in  value  between  an  acre  of  land  and  a  share  of  bank  stock? 

5.  How  many  bushels  of  wheat,  worth  88  cents  a  bushel, 
are  worth  as  much  as  3648  bushels  of  corn,  at  33  cents  a 
bushel? 

6.  Paid  $7500  for  125  acres  of  land.     Cost  per  acre? 

7.  How  long  will  it  take  a  vessel  to  sail  from  New  York 
to  China,  if  the  distance  be  9028  miles,  and  the  ship  sail  148 
miles  a  day? 

8.  A  man  paid  $170352  for  36  city  lots.     What  was  the 
average  cost  per  lot? 

9.  463455  -f-  125.  36.  194378  -i-  562. 

10.  346876  -f-  128.  37.  486327  •+-  641. 

11.  568942  -f-  276.  38.  346845  -~  725. 

12.  654363  -r-  326.  39.  428336  -r-  841. 

13.  784354  -r-  432.  40.  635842  -r-  913. 

14.  584364  -r-  356.  26.  198764  -5-  648. 

15.  635207  -r-  374.  27.  256351  -j-  653. 

16.  657819  -*-  297.  28.  341578  ^  731. 

17.  751682  -*-  431.  29.  462436  -5-  752. 

18.  723156  -5-  453.  30.  521673  -s-  845. 

19.  298764  -f-  468.  31.  534217  -*  873. 

20.  568372  -i-  517.  32.  694738  -r-  958. 


CHAPTER  THREE.  205 

LESSON     LVII. 
REDUCTION    BY    DIVISION. 

1.  How  many  pounds  in  3460  ounces? 

2.  How  many  yards  in  1242  inches? 

3.  How  many  gallons  in  2347  pints? 

4.  How  many  pounds  Troy  in  23547  grains? 

5.  How  many  bushels  in  1597  quarts? 

6.  How  many  pounds  avoirdupois  in  107520  ounces? 

7.  How  many  hours  in  28635  seconds? 

8.  How  many  weeks  in  3561829  seconds? 

9.  How  many  cords  in  67893  cu.  ft.  ? 

10.  How  many  cwt.  in  1491  pounds? 

11.  Keduce  12244  pints  to  hogsheads. 

12.  Eeduce  25600  sq.  rds.  to  acres. 

13.  Eeduce  51200  rds.  to  miles. 

14.  Eeduce  6048  furlongs  to  miles. 

15.  Eeduce  316800  in.  to  miles. 

16.  Eeduce  1435  feet  to  fathoms. 

17.  Eeduce  100000  sheets  of  paper  to  reams. 

18.  Eeduce  27878400  sq.  ft.  to  square  miles. 

19.  Eeduce  85894  grains  to  pounds  Troy? 

20.  Eeduce  51570  pounds  to  tons. 

21.  Change  4536  pounds  of  wheat  to  bushels. 

22.  Change  6912  pounds  of  oats  to  bushels. 

23.  Change  14000  pounds  of  corn  to  bushels. 

24.  Change  43760  cu.  ft.  to  cords. 

25.  Change  70  times  800  acres  to  square  miles. 

26.  Change  168474  ft.  to  miles. 

27.  Change  31556026  seconds  to  days. 

28.  What  is  \  of  10  bu.,  3  pk.,  2  qt.  of  wheat? 

29.  How  many  times  are  4  bu.,  3  pk.,  2  qt.,  contained  in 
336  bu.,  3pk.,  4qt.? 


206  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    LVIII. 

PRINCIPLES. 

Let  the  pupil  be  required  to  illustrate  the  following  prob- 
lems by  original  examples: 

1.  Given,  several  numbers,  to  find  their  sum. 

2.  Given,  the  sum  of  several  numbers  and  all  of  them  but 
one,  to  find  that  one. 

3.  Given,  two  numbers,  to  find  their  difference. 

4.  Given,  the  minuend  and  subtrahend,  to  find  the  remain- 
der. 

5.  Given,  the  minuend  and  remainder,  to  find  the  subtra- 
hend. 

6.  Given,  the  subtrahend  and  remainder,  to  find  the  min- 
uend. 

7.  Given,  two  or  more  numbers,  to  find  their  product. 

8.  Given,  the  multiplicand  and  multiplier,  to  find  the  pro- 
duct. 

9.  Given,  the  product  and  multiplicand,  to  find  the  multi- 
plier. 

10.  Given  the  product  and  multiplier,  to  find  the  multi- 
plicand. 

11.  Given,  two  numbers,  to  find  their  quotients. 

12.  Given,  the  divisor  and  dividend,  to  find  the  quotient. 

13.  Given,  the  divisor  and  quotient,  to  find  the  dividend. 

14.  Given,  the  dividend  and  quotient,  to  find  the  divisor. 

15.  Given,  the  divisor,  quotient  and  remainder,  to  find  the 
dividend. 

16.  Given,  the  dividend,  quotient  and  remainder,  to  find 
the  divisor. 


CHAPTER  THREE.  207 

LESSON    LIX. 

1.  How  is  i  of  an  apple  obtained?    i  of  an  apple  is  ob- 
tained by  dividing  the  apple  into  2  equal  parts  and  taking  one 
of  the  parts. 

2.  How  is  1  of  a  pile  of  sand  obtained?    X  of  a  pile  of 
sand  is  obtained  by  dividing  the  pile  into  2  equal  parts  and 
taking  one  of  the  parts. 

3.  How  is  ^  of  10  oranges  obtained?    i  of  10  oranges  is 
obtained  by  dividing  the  10  oranges  into  2  equal  parts  and 
taking  one  of  the  parts. 

NOTE. — Let  the  pupil  verify  the  above  facts  by  his  own  meas- 
urement 

4.  How  is  1  of  a  unit,  quantity  or  number  obtained?     | 
of  a  unit,  quantity  or  number  is  obtained  by  dividing  the  unit, 
quantity  or  number  into  2  equal  parts  and  taking  one  of  the 
parts. 

5.  What  is  meant  by  -*  of  a  unit,  quantity  or  number?    By 
jL  of  a  unit,  quantity  or  number  is  meant  one  of  the  2  equal 
parts  into  which  the  unit,  quantity  or  number  is  divided. 

6.  How  is  J  of  a  melon  obtained?     2  of  a  melon? 

3  o 

7.  What  is  meant  by  -J  of  a  melon?     §  of  a  melon? 

.  o  o 

8.  What  is  meant  by  the  expression  1  ?     |  ? 

9.  How  is  i  of  8  apples  obtained?      23      8 ; 

10.  What  is  meant  by  1.  of  8  apples?  |?  |j 

11.  What  is  meant  by  the  expression  l?  |?  A? 

12.  How  is  l  of  15  marbles  obtained?  |?  |?     |? 
15.  What  is  meant  by  1  of  1 5  marbles  ?  |  ?  |  ?     |  ? 
14.  What  is  meant  by  the  expression  i  ?  |?  3;     |? 


208  FIRST  BOOK  IN  ARITHMETIC. 

LESSON     LX. 
1.  Show  by  means  of  a  line  how  1  of  6  inches  is  obtained. 


2          3 
6  •        6 


2.  What  is  meant  by  1-  of  aline?     |?     |?     1?     5?  etc. 

3.  What  is  meant  by  the  expression  1?     |?     |?     4?  e^Gt 

4.  How  is   i  of  a  pile  of  wood  obtained?     |?     3?  e^ 

5.  What  is  meant  by  ^  of  a  pile  of  wood  ?     |  ?     |  ?  e^c 
£.  What    is    meant    by  the  expression    ^?     ^?     3?  ^ 

7.  How  is  -J-  of  a  pail   of  water  obtained  ?     |  ?     |  ?  etc. 

O  O  O 

8.  What  is  meant  by  ^  of  a  pail  of  water?      |?     |?  etc. 
P.  What  is  meant  by  the  expression  1?     J-?     |.?     |?  etc. 

10.  How  is  i   of  27  pennies  obtained  ?     |?     |?     |?  etc. 

11.  What  is  meant  by  1  of  27  pennies?     |?     |?     A?  etc. 

J^.  What  is  meant  by  the  expression!?     _|?     |.?     A?  etc. 

y          u          y          y 

13.  How  is  ri0  of  $40  obtained?     ^  ?     ^  ?     ^  ?  etc. 

14.  What  is  meant  by  ^  of  $40?     ^  ?     -^  ?     ^  ?  etc. 

15.  What  is  meant  by  the  expression  yL  ?     T20  ?     T30  ?  etc. 

16.  How  is  ^   of  44  plums  obtained?     ^?      ^  ?  etc. 
J^.  What  is  meant  by  ^  of  44  plums?      ^  ?     ^  etc. 
18.  What  is  meant  by  the  expression  ^  ?      ^  ?      ^  ?  etc. 
1^.  How  is  jL  of    4  apples  obtained?     fyl     T52-?  etc. 
^.  What  is  meant  by  -^  of  .4  apples?      ^?     -a3_?  ctc. 
21  c  What  is  meant  by  the  expression  ^  ?     j2^  ?     r\  •  etc* 


CHAPTER  THREE,  209 

LESSON    LXI. 

1.  6  is  1  of  what  number?     2  of  what  number? 

o  o 

ANALYSIS  :    Since  6  is  %  of  a  number,  1/8  of  the  number  is  Va  of 
6,  which  is  3,  and  3/&  or  the  number  is  3  times  3,  which  is  9. 

2.  8  is  1  of  what  number?     |-  of  what  number? 

5  5 

3.  9  is  I  of  what  number?     £  of  what  number? 

4  4 

4.  10  is  ^  of  what  number?     |  of  what  number? 

5.  12  is  1  of  what  number?     f-  of  what  number? 

o  o 

6.  14  is  |  of  what  number?     t  of  what  number? 

7.  15  is  §  of  what  number?     £  of  what  number? 

7  O 

5.  16  is  A  of  what  number?     ^  of  what  number? 

9.  18  is  |  of  what  number?     ^  of  what  number? 

10.  20  is  |^  of  what  number?  |  of  what  number? 

11.  24  is  r4T  of  what  number?  |  of  what  number? 

12.  36  is  |  of  what  number?  A  of  what  number? 

13.  42  is  |  of  what  number?  1  of  what  number? 

14.  45  is  |  of  what  number?  ^  of  what  number? 

15.  54  is  ^  of  what  number?  -^  of  what  number? 
2£.  56  is  I  of  what  number?  4  °f  what  number? 

8  5 

17.  63  is  5.  of  what  number?     |  of  what  number? 

o  o 

18.  64  is  ^82  of  what  number?     |  of  what  number? 

19.  72  is  4  of  what  number?     £  of  what  number? 

o  y 

£0.  81  is  |  of  what  number?     |  of  what  number? 

21.  84  is  .j«L.  of  what  number?     -^2-  of  what  number? 

22.  96  is  |  of  what  number?    JL2-  of  what  number? 

23.  108  is  9  of  what  number?    JJS.  of  what  number? 
£4.  120  is  i-Q.  of  what  number?     i^2-  of  what  number? 
£5.  132  is  11  of  what  number?     1|-  of  what  number? 
26.  144  is^2_0f  what  number?     *72  of  what  number? 


210  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    LXII. 

1.  If  |  of  a  yard  of  tape  cost  4  cents,  what  is  the  cost  of 

1  yard? 

ANALYSIS:    Since  2/s  of  a  yard  of  tape  costs  4  cents,  Vs  of  a  yard 
costs  Vs  of  4  cents,  which  is  2  cents,  and  s/3,  or  1  yard,  cost  3  times 

2  cents,  which  is  6  cents. 

2.  If  2  of  a  ton  of  coal  cost  $6,  what  is  the  cost  of  1  ton? 

o 

3.  If  A  of  a  box  of  oranges  cost  $6,  what  is  the  cost  of  1 
box? 

4.  What  is  the  cost  of  1  box  of  soap,  if  -|  of  a  box  cost  $9? 

5.  What  is  the  cost  of  a  dining  table,  if  |  of  the  cost  is  $12? 

6.  What  is  the  distance  from  A  to  B,  if  *  Of  the  distance 
is  28  miles? 

7.  How  far  does  he  walk  in  1  day  who  walks  15  miles  in 
|  of  a  day? 

8.  How  old  is  A,  if  A  of  his  age  is  63  years? 

9.  How  much  does  B  owe  C,  if  «  of  the  debt  is  $36? 

10.  How  many  sheep  are  in  a  field,  if  |    of  them  equal  72 
sheep? 

11.  In  how  many  days  can  a  bridge  be  built,  if  i  of  it  can 
be  built  in  63  days? 

12.  How  many  yards  are  in  a  bolt  of  cloth,  if  -^  of  the 
bolt  contains  49  yards? 

13.  In  how  many  days  can  a  man  build  a  wall,  if  he  can 
build  £  of  it  in  56  days  ? 

14.  A  farmer  sold  72  acres  of   land,  which  is  T8^  °*  h*3 
farm.     How  many  acres  were  in  the  farm? 

15.  A  boy  spent  63  cents,  which  is  ^  of  all  he  had.     How 
much  had  he? 

16.  How  much  money  has  A,  if  |  of  his  money  is  $81? 

17.  If  -|  of  a  cord  of  wood  costs  $6,  what  is  the  cost  of  | 
of  a  cord? 


CHAPTER  THREE.  211 

LESSON     LXIII. 

1.  Draw  a  line  six  inches  long  and  divide  it  into  two  equal 
parts.  Tell  why  each  part  is  called  1  of  the  line. 

1  line  equals  how  many  half -lines?  2  lines?  5  lines?  8 
lines?  10  lines?  12  lines? 

1  equals  how  many  halves?   2?   4?    6?    7?    9?    11?    12? 

Divide  the  same  line  into  three  equal  parts  and  tell  why  each 
part  is  called  1  of  the  line. 

1  line  equals  how  many  third-lines?  3  lines?  5  lines?  7 
lines?  9  lines?  11  lines? 

1  equals  how  many  thirds ?     2?     4?     6?     8?     10?     12? 

Examine  the  line  and  tell  which  is  the  greater  part,  l  or  1 , 

lorl? 

Divide  the  same  line  into  four  equal  parts  and  tell  why  each 
part  is  called  i-  of  the  line. 

1  line  equals  how  many  fourth -lines?  1  line?  2  lines?  4 
lines?  6  lines?  8  lines?  10  lines?  12  lines? 

1  equals  how  many  fourths?   -1?    3?   6?   7?    9?    11?    12? 

Examine  the  line  and  tell  which  is  the  greater  part,  1  or  1, 
i  or  I  -J  or  £  §  or  4?  What  two  parts  are  equal? 

o  4*2  4 "     o  4  ,  *  * 

Divide  the  same  line  into  six  equal  parts,  and  tell  why  each 
part  is  called  1  of  the  line. 

1  line  equals  how  many  sixth-lines?  i  line?  1  line?  | 
line?  3  lines?  5  lines?  7  lines?  9  lines? 

1  equals  how  many  sixths  (6ths)?  .X?  1?  |?  2?  4? 
6?  8?  10?  12? 

Draw  a  line  8  inches  long,  divide  it  into  eight  equal  parts 
and  tell  why  each  part  is  called  1  of  a  line.  Divide  the  same 
line  into  halves  and  fourths. 

1  line  equals  how  many  eighth-lines?  1  line?  -1  line?  | 
lines?  3  lines?  5  lines?  7  lines?  9  lines?  11  lines? 


212  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    LXIV. 

Draw  a  line  9  inches  long ;  divide  it  into  nine  equal  parts, 
and  tell  why  each  part  is  called  -1  of  the  line.  Divide  the  same 
line  into  thirds. 

1  line  equals  how  many  ninth -lines?  1  line?  |  lines? 
2  lines?  4  lines?  6  lines?  8  lines?  10  lines?  12  lines? 

1  equals  how  many  ninths?  1?  |?  3?  5?  7?  9? 
11? 

Draw  a  line  10  inches  long;  divide  it  into  ten  equal  parts 
and  tell  why  each  part  is  called  ^1  of  the  line?  Divide  the 
same  line  into  halves  and  fifths. 

1  line  equals  how  many  tenth -lines?  l  line?  1  line? 
I-  lines?  I  lines?  -£  lines?  3  lines?  5  lines?  7  lines? 

555 

9  lines?     11  lines? 

1  equals  how  many  tenths?  1?  1?  |?  |?  |?  2?  4? 
6?  8?  10?  12? 

Draw  a  line  12  inches  long;  divide  it  into  twelve  equal 
parts,  and  tell  why  each  of  these  parts  is  called  ^L-  of  the 
line?  Divide  the  same  line  into  halves,  thirds,  fourths,  and 
sixths. 

1  line  equals  how  many  twelfth -lines?  l  line?  1  line? 
|  lines?  i  line?  |  iines?  |  lines?  1  line?  |  lines? 
g.  lines?  4  lines?  g  lines?  2  lines?  4  lines?  6  lines? 

666 

8  lines?     10  lines?     12  lines? 

1  equals  how  many  twelfths  ?     1  ?     -i  ?     |  ?     1  ?     |  ?     |  ? 

1?       29       |?       49       59      39       59       79       99       H9 

O  D  D  O  O 


CHAPTER  THREE.  213 

LESSON     LXV. 

1.  How  many  halves  are  in     2?     2£?     8?     4£?     5?     6£? 

2.  How.  many  halves  are  in    7?    8£?    9?     10?    11?    12£? 

3.  How  many  thirds  are  in     2^?     3?    4f?    5J?    6|?    8J? 

4.  How  many  fourths  are  in  3|?  4f?   6J?   8|?   9£?   12f? 

5.  How  many  fifths  are  in    3^?    4f?   6|?    7|?    9|?    12|? 

6.  How  many  sixths  are  in  4J?   5|?   7f?    8£?    9£?    11|? 

7.  How  many  sevenths  are  in   3|?   43?   5|?   6|?   7-f?  9^? 

8.  How  many  eighths  are  in  5J?   6§?   7f?   8J?   9f?   12|? 

9.  How  many  ninths  are  in  6|?   7|?   8|?   9J?   11§?  12'? 

10.  How  many  tenths  are  in      5T2y?      65%?      7T%?      6:\? 


I.  How  many  elevenths  are  in    4r2T?     5^  ?     6r4x  ?     7T5T? 
?     9^-? 

-?.  How  many  twelfths  are  in      5^?     6T22?     7-^? 


9f|? 

15.  How  many  are  2  times  J?     3  times  i?     4  times  1? 

14.  How  many  are  5  times  J-?     6  times  -}?     7  times  ^? 

15.  How  many  are  8  times  ^?     9  times  y1,,?     11  times  f-2? 

16.  How  many  are  i  of  f  ?     1  of  f  ?     |  of  |? 
77.  How  many  are  |  of  |?     1  of  4?     |  of  £? 
I<S.  How  many  are  1  of  f  ?     |  of  ^?     y1!  of  ||? 
IP.  How  many  are  4  of  1J?     J  of  If?     J  of  1|? 
m  How  many  are  |  of  1  J  ?     1  of  1  ^  ?     |  of  4f  ? 
^1.  How  many  are  J  of  4£  ?    J-  of  7|?     ^  of  5|? 

^.  How  many  ones  equal  |?     -|?     j?     f?     y?    -1/? 
^5.  How  many  ones  equal  I?     -1/-?     Y?     ^-?     ¥? 
^4.  How  many  ones  equal  \2-?     ^?     -3/?     -&0-?    -4/?    -5/? 
25.  How  many  ones  equal  -375-?    -874-?    -5¥6-?    -7827?     Y?    -HP? 
^6.  How  many  ones  equal  f  |?   -^?   ff?   JT3-r?   fl?  JiV'? 


214  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    LXVI. 

1.  A  hoy  spent  $|  for  a  book  and  $1  for  a  slate.     How 
much  did  he  spend  for  both? 

2.  James  rode  |  of  a  mile  and  walked  |  of  a  mile.     How 
far  did  he  travel? 

3.  John's  father  gave  him  $ |  and  his  mother  $|.     How 
much  was  given  him? 

4.  Sold  4  of  an  acre  to  one  man  and  £  to  another.     How 

y  y 

much  was  sold  to  both? 

5.  A  ran  ^  of  a  mile  and  B  ran  ^  of  a  mile.     How  far 
did  they  both  run? 

6.  If  B  pays  -|  of  the  cost  of  a  carriage  and  C  pays  the  re- 
mainder, how  much  does  C  pay? 

7.  D  rode  1  mile,  walked  |  of  a  mile  and  ran  1  of  a  mile. 
How  far  did  he  travel? 

8.  John  earned  $1  Monday,  $|  Tuesday  and  $|  Wednes- 
day.    How  much  did  he  earn? 

9.  James  lost  $|  Monday,  $|  Tuesday  and  $|  Wednes- 
day.    How  much  did  he  lose? 

10.  A  bought  at  one  time  11  yards  of  cloth,  at  another  | 
yards.     How  many  yards  did  he  buy? 

11.  Paid  $-i-l  for  a  book  and  $-^  for  a  paper.    How  much 
more  was  paid  for  the  book  than  for  the  paper? 

12.  A  traveled  ^  of  a  mile,  and  B  in  the  opposite  direc- 
tion T5^  of  a  mile.     How  far  apart  are  they  then  ? 

13.  i   of   a  merchant's  goods  were   damaged   by  water. 
What  part  were  saved? 

14.  A  bought  ^L  of  a  farm,  B  ^  and  C  the  remainder. 
What  part  of  the  farm  did  C  buy? 

15.  3.   of  an  estate  was  given  to  a  son,  T5^  to  a  daughter, 
and  the  remainder  to  the  wife.     What  part  of  the  estate  did 
the  wife  get? 


CHAPTER  THREE.  215 

LESSON    LXVII. 

1.  What  is  the  cost  of  3  yards  of  cloth,  if  1  yard  costs  $2  g 

2.  If  1  basket  of  peaches  cost  $.|,  what  is  the  cost  of  4 
baskets  ? 

3.  What  is  the  cost  of  5  pounds  of  tea,  if  1  pound  cost  $ |  ? 

4.  If  1  boy  earns  $|,  at  the  same  rate  how  much  do  6  boys 
earn? 

5.  What  is  the  distance  7  times  round  an  island,  if  the  dis- 
tance once  around  it  is  |-  miles  ? 

6.  If  1  pen  knife  is  worth  $|-,  what  is  the  value  of  8  such 
knives  ? 

7.  How  far  do  8  men  carry  a  load,  if  each  man  carries  it 
^  miles? 

8.  If  1  bushel  of  corn  is  worth  f  T8^,  what  are  9  bushels 
worth? 

9.  How  far  does  a  boy  walk  in  11  hours,  if  he  walks  ^ 
of  a  mile  each  hour? 

10.  If  1  man  can  dig  -|  of  a  rod  of  ditch  in  one  day  how 
much  can  12  men  dig  in  the  same  time? 

11.  What  is  the  cost  of  5  books,  if  2  books  cost  $|? 

12.  If  3  men  can  earn  f -J.  an  hour,  how  much  can  4  men 

o 

earn  in  the  same  time? 

13.  What  is  the  cost  of  9  pine  apples,  if  4  pine  apples 
cost  $|? 

14.  If  3  cwt.  of  hay  cost  $T9Q,  what  is  the  cost  of  10  cwt.? 

15.  What  is  the  cost  of  7  melons,  if  3  melons  cost  f  £? 

16.  If  2  brushes  cost  $T8T,  what  is  the  cost  of  11  brushes? 

17.  What  is  the  cost  of  6  plates,  if  5  plates  cost  f -|£? 
'  18.  If  7  boxes  cost  $|-|,  what  is  the  cost  of  9  boxes? 


216  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    LXVIII. 

CANCELLATION. 

1.  How  many  cords  of  wood  can  be  piled  into  a  shed  that 
is  48  ft.  long,  24  ft.  wide,  and  16  ft.  high? 

SUGGESTION  :  The  capacity  of  the  shed  is  a  number  of  cubic 
feet  equal  to  the  product  of  48  X  24  X  16. 

The  contents  of  a  cord  of  wood  is  a  number  of  cubic  feet  equal 
to  the  product  of  8X4X4. 

The  capacity  of  the  shed  is  the  dividend. 

The  contents  of  a  cord  of  wood  is  the  divisor. 

Instead  of  combining  these  sets  of  factors  into  products,  the 
division  may  be  performed  by  dividing  the  factors  of  the  dividend 
by  the  factors  of  the  divisor,  thus  : 

JB_  X  _6_  X    4  =  144  Cords,  Ans. 
48  X  24  X  16 
8X4X4 

This  method  of  division  is  called  Cancellation,  since  it  consists 
in  striking  out  equal  factors  from  dividend  and  divisor. 

In  actual  practice  the  "striking  out"  process  is  indicated  thus: 

664 


-8-  X  -4-   X  -4- 

Division  by  cancellation  should  be  practiced  whenever  the  divi- 
dend and  divisor,  either  or  both,  consist  of  factors  common  to  both. 

2.  The  factors  of  a  dividend  are  16,  21,  33  and  45;  of  the 
divisor  5,  7,  11  and  15;  what  is  the  quotient? 

3.  How  many  barrels  of  flour  at  $9  a  barrel  must  be  given 
for  27  yards  of  cloth  at  $4  a  yard? 

4.  How  muny  bushels  of  apples  at  75  cents  a  bushel  will 
pay  for  85  pounds  of  coffee  at  30  cents  a  pound? 

5.  A  farmer  exchanged  45  bushels  of  potatoes  worth  40 
cents  a  bushel  for  18  pounds  of  tea.     What  was  the  tea  worth 
a  pound? 


CHAPTER  THREE.  217 

LESSON    LXIX. 

1.  How  many  tons  of  hay  at  $9  a  ton,  must  be  given  for 
27  cords  of  wood,  at  $4  a  cord? 

2.  How  many  bushels  of   corn,  worth  60  cents  a  bushel, 
must  be  given  for  25  bushels  of  rye,  worth  90  cents  a  bushel? 

3.  How  many  peaches,  worth  2  cents  each,  must  be  given 
for  48  oranges,  at  3  cents  each? 

4.  How  many  days'  work,  at  75  cents  a  day,  will  pay  for  80 
pounds  of  coffee,  at  15  cents  a  pound? 

5.  How  many  suits  of  clothes,  at  $24  a  suit,  can  be  made 
from  5  pieces  of  cloth,  each  containing  48  yards,  at  $3  a  yard? 

6.  How  many  tubs  of  butter,  each  containing  48  pounds, 
at  14  cents  a  pound,  must  be  given  for  3  boxes  of  tea,  each 
containing  42  pounds,  worth  60  cents  a  pound? 

7.  A  laborer  gave  12  days'  work  for  48  bushels  of  potatoes, 
worth  50  cents  a  bushel.     What  were  his  daily  earnings? 

8.  A  grocer  sold   24  boxes  of    soap,  each  containing   55 
pounds,  at  10  cents  a  pound,  and  received  as  pay  88  barrels 
of  apples,  each  containing  3  bushels.     How  much  were  the 
apples  worth  a  bushel? 

9.  Sold  20  pounds  of  butter  at  57  cents  a  pound,  which 
exactly  paid  for  15  pounds  of  coffee.     What  was  the  price  of 
the  coffee  a  pound? 

10.  A  merchant  bought  6  loads  of  oats,  each  load  contain- 
ing 22  bags,  and  each  bag  2  bushels,  worth  56  cents  a  bushel. 
He  gave  in  payment   8  boxes  of  tea,   each   containing  21 
pounds.     What  was  the  tea  worth  a  pound? 

11.  How  many  bushels  of  oats  at  $.60  a  bushel,  will  pay 
for  12  tons  of  coal  at  $7.20  a  ton? 

12.  How  many  firkins  of  butter,  each  containing  56  pounds, 
at  13  cents  a  pound,  must  be  given  for  4  barrels  of  sugar, 
sach  containing  182  pounds,  at  6  cents  a  pound? 


218  FIRST  BOOK  IN  ARITHMETIC. 

LESSON     LXX. 

1.  How  many  days'  work,  at  84  cents  a  day,  will  pay  for 
36  bushels  of  corn,  worth  56  cents  a  bushel? 

2.  A  farmer  exchanged  60  bushels  of  oats,  worth  45  cents 
a  bushel,  for  25  pounds  of  tea;    what  was  the  tea  worth  a 
pound? 

8.  A  grocer  bought  12  pounds  of  cheese,  at  9  cents  a  pound, 
and  paid  in  molasses,  at  45  cents  a  gallon;  how  many  gallons 
of  molasses  paid  for  the  cheese? 

4.  Gave  12  barrels  of  Hour,  at  $7  a  barrel,  for  hay  worth 
$18  a  ton;  how  many  tons  of  hay  was  the  flour  worth? 

5.  Sold  8  firkins  of  butter,  each  weighing  56  pounds,  at  15 
cents  a  pound,  and  received  in  payment  3  boxes  of  tea,  each 
containing  40  pounds;  what  was  the  tea  worth  a  pound? 

6.  A  man  took  6  loads  of  apples  to  market,  each  load  con- 
taining 14  barrels,  and  each  barrel  3  bushels.     He  sold  them 
at  50  cents  a  bushel,  and  received  in  payment  9  barrels  of 
sugar,  each  weighing  210  pounds;  what  was  the  sugar  worth 
a  pound? 

7.  A  grocer  sold   12   boxes  of   soap,  each   containing  51 
pounds,  at  10  cents  a  pound;  he  received  in  payment  a  certain 
number  of  barrels  of  potatoes,  each  containing  3  bushels,  at 
30  cents  a  bushel;  how  many  barrels  did  he  receive? 

5,  A  man  sold  4  loads  of  barley,  each  load  containing  60 
bushels,  at  70  cents  a  bushel,  and  received  in  payment  2 
pieces  of  cloth,  each  piece  containing  35  yards;  what  was  the 
cloth  worth  a  yard? 

9.  How  many  bales  of  cloth,  each  containing  40  pieces,  and 
each  piece  containing  36  yards,  worth  $3  a  yard,  must  be 
given  for  120  government  bonds,  worth  $108  each? 

10.  How  many  barrels  of  potatoes,  each  containing  3  bush- 
els, worth  40  cents  a  bushel,  will  pay  for  12  boxes  of  soap, 
each  containing  51  pounds,  worth  10  cents  a  pound? 


CHAPTER  THREE.  219 

LESSON     LXXI. 
INTEREST. 

1.  When  the  interest  of  $100  for  one  year  is  $ 6,  what  is 
the  interest  of  $200  for  the  same  time?      $300?      $400? 
$700?      $1000? 

2.  At  the  rate  of  $6  for  the  use  of  $100,  what  is  the  inter- 
est of  $50?      $25?      $20?      $10? 

3.  Interest  is  money  paid  for  the  use  of  money. 

4.  A  man  borrows  $100  for  one  year,  and  agrees  to  pay  6 
per  cent,  interest.     How  much  does  he  owe  at  the  end  of  the 
year?     He  owes  the  $100  which  he  borrowed,  and  $6  for  the 
use  of  the  same. 

5.  The  $100  is  called  principal.     The  $6  is  called  interest. 
The  principal  and  interest  united  ($106),  is  called  amount. 

6.  Principal  is  money  for  the  use  of  which  interest  is  paid. 

7.  In  computing  interest  the  unit  of  time  is  one  year. 

8.  Six  per  cent,  interest  means  $6  for  the  use  of  $100  one 
year.     Five  per  cent,  interest  means  $5  for  the  use  of  $100 
one  year.     Ten  per  cent,  interest  means  $10  for  the  use  of 
$100  one  year. 

9.  What  is  meant  by  four  per  cent,  interest?     Seven  per 
cent.  ?     Eight  per  cent.  ? 

10.  The  terms  used  in  this  lesson  are  Principal,  Interest, 
Rate  per  cent.,  and  Time. 

11.  At  6  per  cent.,  what  is  the  interest  of  $1  for  one  year? 
$2?      $3?      $5?      $7?      $11? 

12.  At  5  per  cent.,  what  is  the  interest  of  $1  for  one  year? 
$2?      $3?      $6?      $8?      $12? 

13.  At  7  per  cent.,  what  is  the  interest  of  $1  for  one  year? 
$2?      $3?      $5?      $8?      $9? 

14.  At  8  per  cent  ,  what  is  the  interest  of  $1  for  one  year? 
$10?      $20?      $30?      $40?      $50? 


220  FIRST  BOOK  IN  ARITHMETIC. 

LESSON    LXXII. 

1.  At  6  per  cent.,  what  is  the  interest  of  $375  for  one  year? 

SUGGESTION  :       $375  =  $300  +  $50  -f  $25. 
Interest  of  $300=  $18. 
Interest  of  $   50  =  $   3. 
Interest  of  $   25  =  $   1.50. 

Interest  of  $375  =  $22. 50. 

2.  At  8  per  cent.,  what  is  the  interest  of  $425  for  one  year? 

3.  At  7  per  cent.,  what  is  the  interest  of  $775  for  one  year? 

4.  At  5  per  cent.,  find  one  year's  interest  of  $285. 

5.  At  4  per  cent.,  find  the  annual  interest  of  $475. 

6.  At  6  per  cent.,  what  is  one  year's  interest  of  $100? 
2  years?     3  years?     4  years?     5  years?     6  years? 

7.  At  4  per  cent.,  what  is  two  years'  interest  of  $100? 
4  years?     6  years?     8  years  ?     10  years? 

8.  What  is  the  interest  of  $300  for  3  years  at  8  per  cent? 

9.  Find  the  interest  of  $400  for  2  years  at  7  per  cent. 

10.  A  man  borrows  $500  for  3  years,  and  agrees  to  pay  5 
per  cent,  interest.     What  was  due  at  the  end  of  the  3  years? 

SUGGESTION:    Find  the  interest.     Then  find  the  amount. 

12.  How  much  is  due  on  a  debt  of  $600  on  interest  for  2 
years  at  6  per  cent? 

13.  A  was  $800  in  debt  to  B  for  3  years  at  5  per  cent,  inter- 
est.    How  much  was  due  B  at  the  end  of  the  time? 

14.  G  loaned  D  $900  for  4  years  at  8  per  cent.    How  much 
should  D  receive  at  the  expiration  of  the  time? 

15.  How  much  should  one  man  pay  to  another  for  a  loan 
of  $1000  for  5  years  at  10  per  cent? 


CHAPTER  THREE.  221 

LESSON    LXIII. 

1.  When  $6  is  the  interest  for  1  year,  what  is  the  interest 
for  6  months?   4  months?   2  months?   8  months?    10  months? 

2.  At  6  per  cent.,  find  the  interest  of 

$125  for  1  year  6  months. 
$146  for  2  years  8  months. 
$175  for  3  years  10  months. 
$225  for  1  year  2  months. 
$290  for  2  years  4  months. 

3.  The  interest  of  $1  for  12  months,  at  6  percent.,  is  $.06. 
What  is  the  interest  for  1  month?     3  months?     5  months? 
7  months?     9  months?     11  months? 

4.  The  interest  of  $1  for  1  month,  or  30  days,  at  6  per 
cent.,  is  5  mills  (f  .005).     What  is  the  interest  for  6  days? 
12  days?     18  days?     24  days? 

5.  Find  the  interest  of  $150  for  3  years,  10  months,  24 
days,  at  6  per  cent. 

OPERATION:  Interest  of  $1.  6  years=$.18. 
Interest  of  $1.  10  mos.  =$.05. 
Interest  of  $1.  24  days  =$.004. 

$.234. 
$.234X150=$35.10  Int.    Ans. 

Find  6  per  cent,  interest  of 

6.  $50  for  1  year,  2  months,  6  days. 

7.  $65  for  1  year,  3  months,  12  days. 

8.  $75  for  2  years,  4  months,  18  days. 

9.  $132  for  1  year,  7  months,  24  days. 

10.  $175  for  3  years,  6  months,  12  days. 

11.  $250  for  2  years,  6  months,  24  days. 

12.  $325  for  2  years,  5  months,  6  days. 

13.  $412  for  2  years,  9  months,  18  days. 

14.  $450  for  3  years,  8  months,  24  days. 

15.  $1,000  for  6  years,  6  months,  6  days. 


APPRNDIX. 

[Prepared   at  the   suggestion   of  Mr.  ADOLF  KBAUS,  Ex-President  Chicago 
Board  of  Education.] 

Rapidity  in  obtaining  results  in  number  work  should  be 
secured  to  the  pupil  at  every  suitable  stage  of  his  progress 
and  development.  Lesson  XL  VII.,  Chapter  Two,  page  120, 
contains  examples  involving  the  two  operations  of  Addition 
and  Subtraction.  In  such  questions,  time  and  mechanical 
labor  are  saved  by  combining  the  two  processes  into  one, 
that  of  Addition,  as  shown  by  the  solution  in  the  Lesson 
referred  to. 

By  a  like  process  of  Addition  the  successive  remainders  in 
Long  Division  may  be  readily  obtained. 

OPERATION. 

1.  26588  -r-  46  =  578.  Let  the  arrangement  of  terms 

358  be  that  of  an  equation. 

3(38  The  operation  may  be  recited 

368  thus: 

265-:-46=5.     Five  6's  are  30.     30  and  5  are   35.     Write  5  re- 

mainder.   Five  4's  are  20.    20  +  3   and  5  =  26. 

Write  3  remainder. 
358-i-46=7.    Seven  6's  =  42.   42  and  6=  48.    Write  6  remainder. 

Seven  4's  =  28.     28  +  4   and   5  =  35.      Write  3 

remainder. 
368-^-46=8.    Eight  6's  =  48.     No  remainder.      Eight  4's=32. 

32  +  4=36.    No  remainder. 

2.  2081734~-4346=:479. 

34333  Let  the  pupil  "think  out  loud," 

thus: 


4346  in  20817  4  times. 

4  times  6  are  24  and  3  are  27.     (Writes  3  remainder.) 

4  times  4  are  16,  with  2  to  carry;  18  and  3  are  21.     (Writes 

3  remainder.) 

4  times  3  are  12,  with  2  to  carry;  14  and  4  are  18.     (Writes 

4  remainder.) 

4  times  4  are  16,  with  one  to  carry;  17  and  3  are  20.  (Writes 
3  remainder.) 


APPENDIX.  223 

To  the  remainder  3433  bring  down  3  for  the  second  partial  divi- 
dend. 
4346  in   34333,  7  times. 

7  times  6  are  42  and  1  are  43.     (Writes  1  remainder.) 

7  times  4  are  28,  with  4  to  carry,  32,  and  1  are  33.     (Writes 

1  remainder.) 
7  times  3  are  21,  with  3  to  add,  24  and  9  are  33.     (Writes  9 

remainder.) 
7  times  4  are  28,  with  3  to  add;  31  and  3  are  34.     (Writes  3 

remainder.) 

To  the  remainder  3911  bring  down  4  for  the  third  partial  dividend. 
4346  in  39114,  9  times. 

9  times  6  are  54.     (No  remainder. ) 

9  times  4  are  36,  with  5  to  add,  are  41.  (No  remainder.) 
9  times  3  are  27,  with  4  to  add,  are  31.  (No  remainder,) 
9  times  4  are  36,  with  3  to  add,  are  39.  (No  remainder.) 

Let  the  pupil  recite  the  operations  performed  in  the  follow- 
ing divisions : 

3.     423728-^-746=568.  5.     500000-^-675=740. 

"5072  ~2750 


5968  500 

4.     425852^-469=908.-          6.  288888776-^-46237=6248 
3752  114667 

221937 
369896 

The  pupil  should  now  be  able  to  find  the  remainder  for 
himself. 

7.  15946-r-37=458.  9.     103375-r-125=827. 

8.  47085-^-73=645.  10.     324864-^423=768. 

Pupils  may  now  be  required  to  perform  the  examples  on 
pp.  203  and  204  by  the  process  here  presented. 


LIBRARY 


30m-l,'l5 


YB   174 


2 


